MORGAN STANLEY DEAN WITTER US GOVERNMENT MONEY MARKET TRUST
497, 1999-03-31
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<PAGE>
                                                     PROSPECTUS - MARCH 29, 1999
 
Morgan Stanley Dean Witter
                                              U.S. GOVERNMENT MONEY MARKET TRUST
 
                                 [COVER PHOTO]
 
                                       A MONEY MARKET FUND THAT SEEKS TO PROVIDE
                                             SECURITY OF PRINCIPAL, HIGH CURRENT
                                                            INCOME AND LIQUIDITY
 
  The Securities and Exchange Commission has not approved or disapproved these
securities or passed upon the adequacy of this PROSPECTUS. Any representation to
                      the contrary is a criminal offense.
<PAGE>
CONTENTS
 
<TABLE>
<S>                       <C>                                                     <C>
The Fund                  Investment Objectives.................................                   1
                          Principal Investment Strategies.......................                   1
                          Principal Risks.......................................                   2
                          Past Performance......................................                   3
                          Fees and Expenses.....................................                   4
                          Fund Management.......................................                   5
 
Shareholder Information   Pricing Fund Shares...................................                   6
                          How to Buy Shares.....................................                   6
                          How to Exchange Shares................................                   8
                          How to Sell Shares....................................                  10
                          Distributions.........................................                  12
                          Tax Consequences......................................                  13
Financial Highlights      ......................................................                  14
 
Financial Statements --
January, 1999             ......................................................                  15
 
Our Family of Funds       ......................................................   Inside Back Cover
 
                          THIS PROSPECTUS CONTAINS IMPORTANT INFORMATION ABOUT THE FUND. PLEASE READ
                          IT CAREFULLY AND KEEP IT FOR FUTURE REFERENCE.
</TABLE>
 
           FUND CATEGORY
           ---------------------------
       / / Growth
 
       / / Growth and Income
 
       / / Income
 
       /X/ MONEY MARKET
<PAGE>
(SIDEBAR)
MONEY MARKET
A MUTUAL FUND HAVING THE GOAL TO SELECT SECURITIES TO PROVIDE CURRENT INCOME
WHILE SEEKING TO MAINTAIN A STABLE SHARE PRICE OF $1.00.
YIELD
THE FUND'S YIELD REFLECTS THE ACTUAL INCOME THE FUND PAYS TO YOU EXPRESSED AS A
PERCENTAGE OF THE FUND'S SHARE PRICE. BECAUSE THE FUND'S INCOME FROM ITS
PORTFOLIO SECURITIES WILL FLUCTUATE, THE INCOME IT IN TURN DISTRIBUTES TO YOU
AND THE FUND'S YIELD WILL VARY.
(END SIDEBAR)
 
THE FUND
 
ICON  INVESTMENT OBJECTIVES
- --------------------------------------------------------------------------------
           Morgan Stanley Dean Witter U.S. Government Money Market Trust (the
           "Fund") is a money market fund that seeks to provide security of
           principal, high current income and liquidity. There is no guarantee
           that the Fund will achieve these objectives.
 
ICON  PRINCIPAL INVESTMENT STRATEGIES
- --------------------------------------------------------------------------------
             The Fund will invest in high quality, short-term U.S. Government
             securities. The Fund's "Investment Manager," Morgan Stanley Dean
             Witter Advisors Inc., seeks to maintain the Fund's share price at
             $1.00. The share price remaining stable at $1.00 means that the
             Fund would preserve the principal value of your investment.
 
             The U.S. Government securities that the Fund may purchase include:
                            - U.S. Treasury bills, notes and bonds, all of which
                              are direct obligations of the U.S. Government.
                            - Securities issued by agencies and
                              instrumentalities of the U.S. Government which are
                              backed by the full faith and credit of the United
                              States. Among the agencies and instrumentalities
                              issuing these obligations are the Government
                              National Mortgage Association and the Federal
                              Housing Administration.
                            - Securities issued by agencies and
                              instrumentalities which are not backed by the full
                              faith and credit of the United States, but whose
                              issuing agency or instrumentality has the right to
                              borrow, to meet its obligations, from U.S.
                              Treasury. Among these agencies and
                              instrumentalities are the Federal National
                              Mortgage Association, the Federal Home Loan
                              Mortgage Corporation and the Federal Home Loan
                              Banks.
                            - Securities issued by agencies and
                              instrumentalities which are backed solely by the
                              credit of the issuing agency or instrumentality.
                              Among these agencies and instrumentalities is the
                              Federal Farm Credit System.
 
             The Fund also may invest up to 10% of its assets in FDIC insured
             certificates of deposit of banks and saving and loan institutions.
 
             The Fund's policies discussed above are fundamental. These policies
             may not be changed without shareholder approval. In addition to the
             fundamental investment policies, the Fund may invest in repurchase
             agreements. Repurchase agreements are contracts in which a
             financial institution sells a security and agrees to buy it back on
             a specific date (usually within 7 days) and at a higher price,
             which reflects an agreed-upon interest rate.
 
                                                                               1
<PAGE>
ICON  PRINCIPAL RISKS
- --------------------------------------------------------------------------------
 
            CREDIT AND INTEREST RATE RISKS. A principal risk of investing in the
             Fund is associated with its U.S. Government securities investments,
             which are subject to two types of risks: credit risk and interest
             rate risk. Credit risk refers to the possibility that the issuer of
             a security will be unable to make interest payments and repay the
             principal on its debt. Interest rate risk, another risk of debt
             securities, refers to fluctuations in the value of a fixed-income
             security resulting from changes in the general level of interest
             rates.
 
             Credit risk is minimal with respect to the Fund's U.S. Government
             securities investments. Repurchase agreements involve a greater
             degree of credit risk. The Investment Manager, however, actively
             manages the Fund's assets to reduce the risk of losing any
             principal investment as a result of credit or interest rate risks.
             In addition, federal regulations require money market funds, such
             as the Fund, to invest only in debt obligations of high quality and
             short maturities.
 
             An investment in the Fund is not a deposit of a bank and is not
             insured or guaranteed by the FDIC or any other government agency.
             Although the Fund seeks to preserve the value of your investment at
             $1.00 per share, if it is unable to do so, it is possible to lose
             money by investing in the Fund.
 
            YEAR 2000. The Fund could be adversely affected if the computer
             systems necessary for the efficient operation of the Investment
             Manager, the Fund's other service providers and the markets and
             individual and governmental issuers in which the Fund invests do
             not properly process and calculate date-related information from
             and after January 1, 2000. While year 2000-related computer
             problems could have a negative effect on the Fund, the Investment
             Manager and affiliates are working hard to avoid any problems and
             to obtain assurances from their service providers that they are
             taking similar steps.
 
2
<PAGE>
   
(SIDEBAR)
ANNUAL TOTAL RETURNS
THIS CHART SHOWS HOW THE PERFORMANCE OF THE FUND'S SHARES HAS VARIED FROM YEAR
TO YEAR OVER THE PAST 10 CALENDAR YEARS.
    
AVERAGE ANNUAL
TOTAL RETURNS
THIS TABLE COMPARES THE FUND'S AVERAGE ANNUAL RETURNS WITH THOSE OF A BROAD
MEASURE OF MARKET PERFORMANCE OVER TIME.
(END SIDEBAR)
 
ICON  PAST PERFORMANCE
- --------------------------------------------------------------------------------
           The bar chart and table below provide some indication of the risks of
           investing in the Fund. For the Fund's most recent 7-day annualized
           yield, you may call (800) 869-NEWS. The Fund's past performance does
           not indicate how the Fund will perform in the future.
 
ANNUAL TOTAL RETURNS - CALENDAR YEARS
 
[CHART]
 
During the periods shown in the bar chart, the highest return for a calendar
quarter was 2.22% (quarter ended June 30, 1989) and the lowest return for a
calendar quarter was 0.55% (quarter ended June 30, 1993).
 
<TABLE>
<CAPTION>
AVERAGE ANNUAL TOTAL RETURNS (FOR THE PERIODS ENDED THE 1998 CALENDAR YEAR)
- -------------------------------------------------------------------------------
                                     PAST 1 YEAR   PAST 5 YEARS   PAST 10 YEARS
<S>                                  <C>           <C>            <C>
- -------------------------------------------------------------------------------
 U.S. Government Money Market           4.71%         4.41%           4.85%
- -------------------------------------------------------------------------------
 Lipper U.S. Government Money
 Market Funds Index(1)                  4.95%         4.79%           5.19%
- -------------------------------------------------------------------------------
</TABLE>
 
1    The Lipper U.S. Government Money Market Funds Index is an equally-weighted
     performance index of the largest qualifying funds (based on net assets) in
     the Lipper U.S. Government Money Market Funds objective. The index, which
     is adjusted for capital gains distributions and income dividends, is
     unmanaged and should not be considered an investment. There are currently
     30 funds represented in the index.
 
                                                                               3
<PAGE>
(SIDEBAR)
ANNUAL FUND
OPERATING EXPENSES
THESE EXPENSES ARE DEDUCTED FROM THE FUND'S ASSETS AND ARE BASED ON EXPENSES
PAID FOR THE FISCAL YEAR ENDED JANUARY 31, 1999.
(END SIDEBAR)
 
ICON  FEES AND EXPENSES
- --------------------------------------------------------------------------------
           The Fund is a no-load fund. The Fund does not impose any sales
           charges and does not impose account or exchange fees. The table below
           briefly describes the fees and expenses that you may pay if you buy
           and hold shares of the Fund.
 
<TABLE>
<S>                                                           <C>
 ANNUAL FUND OPERATING EXPENSES
- -----------------------------------------------------------------------
 Management Fee                                                 0.46%
- -----------------------------------------------------------------------
 Distribution and service (12b-1) fees                          0.10%
- -----------------------------------------------------------------------
 Other expenses                                                 0.38%
- -----------------------------------------------------------------------
 Total annual Fund operating expenses                           0.94%
- -----------------------------------------------------------------------
</TABLE>
 
           EXAMPLE
           This example is intended to help you compare the cost of investing in
           the Fund with the cost of investing in other mutual funds.
 
           The example assumes that you invest $10,000 in the Fund, your
           investment has a 5% return each year, and the Fund's operating
           expenses remain the same. Although your actual costs may be higher or
           lower, the table below shows your costs at the end of each period
           based on these assumptions.
 
<TABLE>
<CAPTION>
- ----------------------------------------------------------
                 1 YEAR    3 YEARS    5 YEARS    10 YEARS
<S>              <C>       <C>        <C>        <C>
- ----------------------------------------------------------
                   $ 96      $300       $520       $1,155
- ----------------------------------------------------------
</TABLE>
 
4
<PAGE>
(SIDEBAR)
MORGAN STANLEY DEAN WITTER ADVISORS INC.
THE INVESTMENT MANAGER IS WIDELY RECOGNIZED AS A LEADER IN THE MUTUAL FUND
INDUSTRY AND TOGETHER WITH MORGAN STANLEY DEAN WITTER SERVICES COMPANY INC., ITS
WHOLLY-OWNED SUBSIDIARY, HAS MORE THAN $126.2 BILLION IN ASSETS UNDER MANAGEMENT
OR ADMINISTRATION AS OF FEBRUARY 28, 1999.
(END SIDEBAR)
 
ICON  FUND MANAGEMENT
- --------------------------------------------------------------------------------
             The Fund has retained the Investment Manager -- Morgan Stanley Dean
             Witter Advisors Inc. -- to provide administrative services, manage
             its business affairs and invest its assets, including the placing
             of orders for the purchase and sale of portfolio securities. The
             Investment Manager is a wholly-owned subsidiary of Morgan Stanley
             Dean Witter & Co., a preeminent global financial services firm that
             maintains leading market positions in each of its three primary
             businesses: securities, asset management and credit services. Its
             main business office is located at Two World Trade Center, New
             York, NY 10048.
 
             The Fund pays the Investment Manager a monthly management fee as
             full compensation for the services and facilities furnished to the
             Fund, and for Fund expenses assumed by the Investment Manager. The
             fee is based on the Fund's average daily net assets. For the fiscal
             year ended January 31, 1999 the Fund accrued total compensation to
             the Investment Manager amounting to 0.46% of the Fund's average
             daily net assets.
 
                                                                               5
<PAGE>
(SIDEBAR)
CONTACTING A FINANCIAL ADVISOR
IF YOU ARE NEW TO THE MORGAN STANLEY DEAN WITTER FAMILY OF FUNDS AND WOULD LIKE
TO CONTACT A FINANCIAL ADVISOR, CALL (800) THE-DEAN FOR THE TELEPHONE NUMBER OF
THE MORGAN STANLEY DEAN WITTER OFFICE NEAREST YOU.
YOU MAY ALSO ACCESS OUR OFFICE LOCATOR ON OUR INTERNET SITE AT:
WWW.DEANWITTER.COM/FUNDS
(END SIDEBAR)
 
SHAREHOLDER INFORMATION
 
ICON  PRICING FUND SHARES
- --------------------------------------------------------------------------------
           The price of Fund shares, called "net asset value," is based on the
           amortized cost of the Fund's portfolio securities. The amortized cost
           valuation method involves valuing a debt obligation in reference to
           its cost, rather than market forces.
 
           The net asset value per share of the Fund is determined once daily at
           4:00 p.m. Eastern time on each day that the New York Stock Exchange
           is open (or, on days when the New York Stock Exchange closes prior to
           4:00 p.m., at such earlier time). Shares will not be priced on days
           that the New York Stock Exchange is closed.
 
ICON  HOW TO BUY SHARES
- --------------------------------------------------------------------------------
             You may open a new account to buy Fund shares or buy additional
             Fund shares for an existing account in several ways. When you buy
             Fund shares, the shares are purchased at the next share price
             calculated after we receive your investment in proper form and
             accompanied by federal or other immediately available funds. You
             begin earning dividends the business day after the shares are
             purchased. We reserve the right to reject any order for the
             purchase of Fund shares.
 
<TABLE>
<CAPTION>
MINIMUM INVESTMENT AMOUNTS
- --------------------------------------------------------------------
                                              MINIMUM INVESTMENT
                                          --------------------------
 INVESTMENT OPTIONS                          INITIAL     ADDITIONAL
<S>                                       <C>            <C>
- --------------------------------------------------------------------
 Regular Accounts:
                                          $       1,000     $  50
- --------------------------------------------------------------------
 Individual Retirement Accounts:
     Regular IRAs
                                          $       1,000     $  50
- --------------------------------------------------------------------
     Education IRAs
                                          $         500     $  50
- --------------------------------------------------------------------
 EASYINVEST -SM- (Automatically from
 your checking or savings account or
 Money Market Fund)
                                          not available     $ 100
- --------------------------------------------------------------------
</TABLE>
 
             There is no minimum investment amount if you purchase Fund shares
             through: (1) the Investment Manager's mutual fund asset allocation
             plan, (2) a program, approved by the Fund's distributor, in which
             you pay an asset-based fee for advisory, administrative and/or
             brokerage services, or (3) employer-sponsored employee benefit plan
             accounts. In addition, the Fund will waive the minimum initial
             investment for the automatic reinvestment of distributions from
             certain unit investment trusts.
 
6
<PAGE>
 
<TABLE>
<CAPTION>
 INVESTMENT
 OPTIONS            PROCEDURES
<S>                 <C>
- --------------------------------------------------------------------------------
 Contact Your       NEW ACCOUNTS AND SUBSEQUENT INVESTMENTS
 Financial Advisor  You may buy Fund shares by contacting your Morgan Stanley
                    Dean Witter Financial Advisor or other authorized financial
 ICON               representative. Your Financial Advisor will assist you,
                    step-by-step, with the procedures to invest in the Fund.
- --------------------------------------------------------------------------------
 By Mail            NEW ACCOUNTS
 ICON               To open a new account to buy Fund shares:
                    - Complete and sign the attached Application.
                    - Make out a check for the investment amount to: Morgan
                      Stanley Dean Witter U.S. Government Money Market Trust.
                    - Mail the Application and check to Morgan Stanley Dean
                      Witter Trust FSB at P.O. Box 1040, Jersey City, New Jersey
                      07303.
                    ------------------------------------------------------------
                    SUBSEQUENT INVESTMENTS
                    To buy additional shares for an existing Fund account:
                    - Write a "letter of instruction" to the Fund specifying the
                      name(s) on the account, the account number and the social
                      security or tax identification number, and the additional
                      investment amount. The letter must be signed by the
                      account owner(s).
                    - Make out a check for the investment amount to: Morgan
                      Stanley Dean Witter U.S. Government Money Market Trust.
                    - Mail the letter and check to Morgan Stanley Dean Witter
                      Trust FSB at the same address as for new accounts.
- --------------------------------------------------------------------------------
 By wire            NEW ACCOUNTS
 ICON               To open a new account to buy Fund shares:
                    - Mail the attached Application, completed and signed, to
                      Morgan Stanley Dean Witter Trust FSB at P.O. Box 1040,
                      Jersey City, New Jersey 07303.
                    - Before sending instructions by wire, call us at (800)
                      869-NEWS advising us of your purchase and to confirm we
                      have received your Application.
                    - Wire the instructions specifying the name of the Fund and
                      your account number, along with the additional investment
                      amount, to The Bank of New York, for credit to the account
                      of "Morgan Stanley Dean Witter Trust FSB, Harborside
                      Financial Center, Plaza Two, Jersey City, New Jersey
                      07303, Account No. 8900188413."
                    (When you buy Fund shares, wire purchase instructions
                    received by Morgan Stanley Dean Witter Trust FSB prior to
                    12:00 noon Eastern time are normally effective that day and
                    wire purchase instructions received after 12:00 noon are
                    normally effective the next business day.)
                    ------------------------------------------------------------
                    SUBSEQUENT INVESTMENTS
                    To buy additional shares for an existing Fund account:
                    - Before sending instructions by wire, call us at (800)
                      869-NEWS advising us of your purchase.
                    - Wire the instructions specifying the name of the Fund and
                      your account number, along with the investment amount, to
                      The Bank of New York, for credit to the account of Morgan
                      Stanley Dean Witter Trust FSB in the same manner as
                      opening an account.
                    (Also, when you buy additional Fund shares, wire purchase
                    instructions received by Morgan Stanley Dean Witter Trust
                    FSB prior to 12:00 noon Eastern time are normally effective
                    that day and wire purchase instructions received after 12:00
                    noon are normally effective the next business day.)
- --------------------------------------------------------------------------------
 EASYINVEST -SM-    NEW ACCOUNTS
 (Automatically     This program is not available to open a new Fund account or
 from your          a new account of another Money Market Fund.
 checking or        ------------------------------------------------------------
 savings            SUBSEQUENT INVESTMENTS
 account)           EASYINVEST-SM- A purchase plan that allows you to transfer
                    money automatically from your checking or savings account on
                    a semi-monthly, monthly or quarterly basis. Contact your
                    Morgan Stanley Dean Witter Financial
ICON
                    Advisor for further information about this service.
- --------------------------------------------------------------------------------
</TABLE>
 
                                                                               7
<PAGE>
           ADDITIONAL PURCHASE INFORMATION. If you are a customer of Dean Witter
           Reynolds or another authorized dealer of Fund shares, you may upon
           request: (a) have the proceeds from the sale of listed securities
           invested in Fund shares the day after you receive the proceeds; and
           (b) pay for the purchase of certain listed securities by automatic
           sale of Fund shares that you own. In addition, if you are a customer
           of Dean Witter Reynolds or another authorized dealer of Fund shares,
           you may have cash balances in your securities account (which do not
           exceed $5,000) automatically invested in shares of the Fund on a
           weekly basis.
 
           PLAN OF DISTRIBUTION. The Fund has adopted a Plan of Distribution in
           accordance with Rule 12b-1 under the Investment Company Act of 1940.
           The Plan allows the Fund to pay distribution fees for the sale and
           distribution of these shares. It also allows the Fund to pay for
           services to shareholders. Because these fees are paid out of the
           Fund's assets on an ongoing basis, over time these fees will increase
           the cost of your investment and may cost you more than paying other
           types of sales charges.
 
ICON  HOW TO EXCHANGE SHARES
- --------------------------------------------------------------------------------
           PERMISSIBLE FUND EXCHANGES. You may only exchange shares of the Fund
           for shares of other continuously offered Morgan Stanley Dean Witter
           Funds if the Fund shares were acquired in an exchange of shares
           initially purchased in a Multi-Class Fund or an FSC Fund (subject to
           a front-end sales charge). In that case, the shares may be
           subsequently re-exchanged for shares of the same Class of any
           Multi-Class Fund or FSC Fund or for shares of another Money Market
           Fund, No-Load Fund or Short-Term U.S. Treasury Trust. Of course, if
           an exchange is not permitted, you may sell shares of the Fund and buy
           another Fund's shares with the proceeds.
 
           See the inside back cover of this PROSPECTUS for each Morgan Stanley
           Dean Witter Fund's designation as a Multi-Class Fund, FSC Fund,
           No-Load Fund or Money Market Fund. If a Morgan Stanley Dean Witter
           Fund is not listed, consult the inside back cover of that Fund's
           PROSPECTUS for its designation. For purposes of exchanges, shares of
           FSC Funds are treated as Class A shares of a Multi-Class Fund.
 
           An exchange privilege account also may be maintained for you if you
           acquired Fund shares in exchange for shares of various TCW/DW Funds.
 
           The current PROSPECTUS for each Fund describes its investment
           objective(s), policies and investment minimums, and should be read
           before investing.
 
           EXCHANGE PROCEDURES. You can process an exchange by contacting your
           Morgan Stanley Dean Witter Financial Advisor or other authorized
           financial representative. Otherwise, you must forward an exchange
           privilege authorization form to the Fund's transfer agent -- Morgan
           Stanley Dean Witter Trust FSB -- and then write the transfer agent or
           call (800) 869-NEWS to place an exchange order. You can obtain an
           exchange privilege authorization form by contacting your Financial
           Advisor or other authorized financial representative or by calling
           (800) 869-NEWS.
 
8
<PAGE>
           An exchange to any Morgan Stanley Dean Witter Fund (except a Money
           Market Fund) is made on the basis of the next calculated net asset
           values of the Funds involved after the exchange instructions are
           accepted. When exchanging into a Money Market Fund, the Fund's shares
           are sold at their next calculated net asset value and the Money
           Market Fund's shares are purchased at their net asset value on the
           following business day.
             The Fund may terminate or revise the exchange privilege upon
             required notice. Certain services normally available to
             shareholders of Money Market Funds, including the check writing
             privilege, are not available for Money Market Fund shares you
             acquire in an exchange.
            TELEPHONE EXCHANGES. For your protection when calling Morgan Stanley
             Dean Witter Trust FSB, we will employ reasonable procedures to
             confirm that exchange instructions communicated over the telephone
             are genuine. These procedures may include requiring various forms
             of personal identification such as name, mailing address, social
             security or other tax identification number. Telephone instructions
             also may be recorded.
             Telephone instructions will be accepted if received by the Fund's
             transfer agent between 9:00 a.m. and 4:00 p.m. Eastern time, on any
             day the New York Stock Exchange is open for business. During
             periods of drastic economic or market changes, it is possible that
             the telephone exchange procedures may be difficult to implement,
             although this has not been the case with the Fund in the past.
            MARGIN ACCOUNTS. If you have pledged your Fund shares in a margin
             account, contact your Morgan Stanley Dean Witter Financial Advisor
             or other authorized financial representative regarding restrictions
             on the exchange of such shares.
            EXCHANGING SHARES OF ANOTHER FUND SUBJECT TO A CONTINGENT DEFERRED
            SALES CHARGE ("CDSC"). There are special considerations when you
             exchange shares subject to a CDSC of another Morgan Stanley Dean
             Witter Fund for shares of the Fund. When determining the length of
             time you held the shares and the corresponding CDSC rate, any
             period (starting at the end of the month) during which you held
             shares of the Fund WILL NOT BE COUNTED. Thus, in effect the
             "holding period" for purposes of calculating the CDSC is frozen
             upon exchanging into the Fund. Nevertheless, if shares subject to a
             CDSC are exchanged for shares of the Fund, you will receive a
             credit when you sell the shares equal to the distribution (12b-1)
             fees, if any, you paid on those shares while in the Fund up to the
             amount of any applicable CDSC. See the PROSPECTUS of the Fund that
             charges the CDSC for more details.
            FREQUENT EXCHANGES. A pattern of frequent exchanges may result in
             the Fund limiting or prohibiting, at its discretion, additional
             purchases and/or exchanges. The Fund will notify you in advance of
             limiting your exchange privileges.
             For further information regarding exchange privileges, you should
             contact your Morgan Stanley Dean Witter Financial Advisor or call
             (800) 869-NEWS.
 
                                                                               9
<PAGE>
(SIDEBAR)
SYSTEMATIC
WITHDRAWAL PLAN
THIS PLAN ALLOWS YOU TO WITHDRAW MONEY AUTOMATICALLY FROM YOUR FUND ACCOUNT AT
REGULAR INTERVALS. CONTACT YOUR MORGAN STANLEY DEAN WITTER FINANCIAL ADVISOR FOR
MORE DETAILS.
(END SIDEBAR)
 
ICON  HOW TO SELL SHARES
- --------------------------------------------------------------------------------
           You can sell some or all of your Fund shares at any time. Your shares
           will be sold at the next share price calculated after we receive your
           order to sell as described below.
 
<TABLE>
<CAPTION>
 OPTIONS            PROCEDURES
<S>                 <C>
- --------------------------------------------------------------------------------
 Contact your       To sell your shares, simply call your Morgan Stanley Dean
 Financial Advisor  Witter Financial Advisor or other authorized financial
 ICON               representative.
                    ------------------------------------------------------------
                    Payment will be sent to the address to which the account is
                    registered or deposited in your brokerage account.
- --------------------------------------------------------------------------------
 Check-writing      You may order a supply of blank checks by requesting them on
 Option             the investment application or by contacting your Morgan
 ICON               Stanley Dean Witter Financial Advisor.
                    ------------------------------------------------------------
                    Checks may be written in any amount not less than $500. You
                    must sign checks exactly as their shares are registered. If
                    the account is a joint account, the check may contain one
                    signature unless the joint owners have specified on an
                    investment application that all owners are required to sign
                    checks.
                    ------------------------------------------------------------
                    Payment of check proceeds normally will be made on the next
                    business day after we receive your check in proper form.
                    Shares purchased by check (including a certified or bank
                    cashier's check) are not normally available to cover
                    redemption checks until fifteen days after Morgan Stanley
                    Dean Witter Trust FSB receives the check used for
                    investment. A check will not be honored in an amount
                    exceeding the value of the account at the time the check is
                    presented for payment.
- --------------------------------------------------------------------------------
 Systematic         If your investment in all of the Morgan Stanley Dean Witter
 Withdrawal Plan    Family of Funds has a total market value of at least
 ICON               $10,000, you may elect to withdraw amounts of $25 or more,
                    or in any whole percentage of a Fund's balance (provided the
                    amount is at least $25), on a monthly, quarterly,
                    semi-annual or annual basis, from any Fund with a balance of
                    at least $1,000. Each time you add a Fund to the plan, you
                    must meet the plan requirements.
                    ------------------------------------------------------------
                    To sign up for the Systematic Withdrawal Plan, contact your
                    Morgan Stanley Dean Witter Financial Advisor or call (800)
                    869-NEWS. You may terminate or suspend your plan at any
                    time. Please remember that withdrawals from the plan are
                    sales of shares, not Fund "distributions," and ultimately
                    may exhaust your account balance. The Fund may terminate or
                    revise the plan at any time.
                    ------------------------------------------------------------
                    When you sell Fund shares through the Systematic Withdrawal
                    Plan, the shares may be subject to a contingent deferred
                    sales charge ("CDSC") if they were obtained in exchange for
                    shares subject to a CDSC of another Morgan Stanley Dean
                    Witter Fund. The CDSC, however, will be waived in an amount
                    up to 12% annually of the Fund's value, although Fund shares
                    with no CDSC will be sold first, followed by those with the
                    lowest CDSC. As such, the waiver benefit will be reduced by
                    the amount of your shares that are not subject to a CDSC.
                    See the PROSPECTUS of the Fund that charges the CDSC for
                    more details.
- --------------------------------------------------------------------------------
</TABLE>
 
10
<PAGE>
<TABLE>
<CAPTION>
 OPTIONS            PROCEDURES
- --------------------------------------------------------------------------------
<S>                 <C>
 By Letter          You may also sell your shares by writing a "letter of
 ICON               instruction" that includes:
                    - your account number;
                    - the dollar amount or the number of shares you wish to
                      sell; and
                    - the signature of each owner as it appears on the account.
                    ------------------------------------------------------------
                    If you are requesting payment to anyone other than the
                    registered owner(s) or that payment be sent to any address
                    other than the address of the registered owner(s) or
                    pre-designated bank account, you will need a signature
                    guarantee. You can obtain a signature guarantee from an
                    eligible guarantor acceptable to Morgan Stanley Dean Witter
                    Trust FSB. (You should contact Morgan Stanley Dean Witter
                    Trust FSB at (800)869-NEWS for a determination as to whether
                    a particular institution is an eligible guarantor.) A notary
                    public CANNOT provide a signature guarantee. Additional
                    documentation may be required for shares held by a
                    corporation, partnership, trustee or executor.
                    ------------------------------------------------------------
                    Mail the letter to Morgan Stanley Dean Witter Trust FSB at
                    P.O. Box 983, Jersey City, NJ 07303.
                    ------------------------------------------------------------
                    A check will be mailed to the name(s) and address in which
                    the account is registered, or otherwise according to your
                    instructions.
- --------------------------------------------------------------------------------
 By Telephone or    You may also sell your shares by calling Morgan Stanley Dean
 Wire               Witter Trust FSB at (800) 869-NEWS or by sending wire
 ICON               instructions to Morgan Stanley Dean Witter Trust FSB at
 ICON               Telex No. 125076. A check will be mailed to the name(s) and
                    address in which the account is registered or, for amounts
                    of $1,000 or more, you may request a wire transfer to the
                    bank account designated in the application.
- --------------------------------------------------------------------------------
</TABLE>
 
           PAYMENT FOR SOLD SHARES. After we receive your complete instructions
           to sell as described above, a check will be mailed to you within
           seven days, although we will attempt to make payment within one
           business day. Payment may also be sent to your brokerage account.
 
           Payment may be postponed or the right to sell your shares suspended,
           however, under unusual circumstances. If you request to sell shares
           that were recently purchased by check, payment of the sale proceeds
           may be delayed for the minimum time needed to verify that the check
           has been honored (not more than fifteen days from the time we receive
           the check).
 
           INVOLUNTARY SALES. The Fund reserves the right, on sixty days'
           notice, to sell the shares of any shareholder whose shares, due to
           sales by the shareholder, have a value below $500. However, before
           the Fund sells your shares in this manner, we will notify you and
           allow you sixty days to make an additional investment in an amount
           that will increase the value of your account to at least the required
           amount before the sale is processed.
 
           MONEY MARKET FUND AUTOMATIC SALE PROCEDURES. If you maintain a
           brokerage account with Dean Witter Reynolds or another authorized
           dealer of Fund shares, you may elect to have your Fund shares
           automatically sold from your account to satisfy amounts you owe as a
           result of purchasing securities or other transactions in your
           brokerage account.
 
           If you elect to participate by notifying Dean Witter Reynolds or
           another authorized dealer of Fund shares, your brokerage account will
           be scanned each business day prior to the close of business (4:00
           p.m. Eastern time). After any cash balances in the account are
           applied, a sufficient number of Fund shares may be sold to satisfy
           any amounts you are obligated to pay to Dean Witter Reynolds or
           another authorized dealer of fund shares.
 
                                                                              11
<PAGE>
(SIDEBAR)
TARGETED DIVIDENDS-SM-
YOU MAY SELECT TO HAVE YOUR FUND DISTRIBUTIONS AUTOMATICALLY INVESTED IN ANOTHER
MORGAN STANLEY DEAN WITTER FUND THAT YOU OWN. CONTACT YOUR MORGAN STANLEY DEAN
WITTER FINANCIAL ADVISOR FOR FURTHER INFORMATION ABOUT THIS SERVICE.
(END SIDEBAR)
Sales will be effected on the business day before the date you are obligated to
make payment, and Dean Witter Reynolds or another authorized dealer of Fund
shares will receive the sale proceeds on the following day.
 
           EASYINVEST -SM- -- AUTOMATIC REDEMPTION. You may invest in shares of
           certain other Morgan Stanley Dean Witter Funds by subscribing to
           EASYINVEST -SM-, an automatic purchase plan that provides for the
           automatic investment of any amount from $100 to $5,000 in shares of
           the specified fund. Under EASYINVEST -SM-, you may direct that a
           sufficient number of shares of the Fund be automatically sold and the
           proceeds transferred to Morgan Stanley Dean Witter Trust FSB, on a
           semi-monthly, monthly or quarterly basis, for investment in shares of
           the specified fund. Sales of your Fund shares will be made on the
           business day preceding the investment date and Morgan Stanley Dean
           Witter Trust FSB will receive the proceeds for investment on the day
           following the sale date.
 
           MARGIN ACCOUNTS. Certain restrictions may apply to Fund shares
           pledged in margin accounts with Dean Witter Reynolds or another
           authorized broker-dealer of Fund shares. If you hold Fund shares in
           this manner, please contact your Morgan Stanley Dean Witter Financial
           Advisor or other authorized financial representative for more
           details.
 
ICON  DISTRIBUTIONS
- --------------------------------------------------------------------------------
           The Fund passes substantially all of its earnings along to its
           investors as "distributions." The Fund earns interest from
           fixed-income investments. These amounts are passed along to Fund
           shareholders as "income dividend distributions." The Fund may realize
           capital gains whenever it sells securities for a higher price than it
           paid for them. These amounts may be passed along as "capital gain
           distributions;" the Investment Manager does not anticipate that there
           will be significant capital gain distributions.
 
           The Fund declares income dividends, payable on each day the New York
           Stock Exchange is open for business, of all of its daily net income
           to shareholders of record as of the close of business the preceding
           business day. Capital gains, if any, are distributed periodically.
 
                            Distributions are reinvested automatically in
                            additional shares of the Fund (rounded to the last
                            1/100 of a share) and automatically credited to your
                            account unless you request in writing that
                            distributions be paid in cash. If you elect the cash
                            option, the Fund will reinvest the additional shares
                            and credit your account during the month, then
                            redeem the credited amount no later than the last
                            business day of the month, and mail a check to you
                            no later than seven business days after the end of
                            the month. No interest will accrue on uncashed
                            checks. If you wish to change how your distributions
                            are paid, your request should be received by the
                            Fund's transfer agent, Morgan Stanley Dean Witter
                            Trust FSB, at least five business days prior to the
                            record date of the distributions.
 
12
<PAGE>
ICON  TAX CONSEQUENCES
- --------------------------------------------------------------------------------
           As with any investment, you should consider how your Fund investment
           will be taxed. The tax information in this PROSPECTUS is provided as
           general information. You should consult your own tax professional
           about the tax consequences of an investment in the Fund.
 
           Unless your investment in the Fund is through a tax-deferred
           retirement account, such as a 401(k) plan or IRA, you need to be
           aware of the possible tax consequences when the Fund makes
           distributions.
 
           Your distributions are normally subject to federal and state income
           tax when they are paid, whether you take them in cash or reinvest
           them in Fund shares. A distribution also may be subject to local
           income tax. Any income dividend distributions and any short-term
           capital gain distributions are taxable to you as ordinary income. Any
           long-term capital gain distributions are taxable as long-term capital
           gains, no matter how long you have owned shares in the Fund.
 
           Every January, you will be sent a statement (IRS Form 1099-DIV)
           showing the taxable distributions paid to you in the previous year.
           The statement provides full information on your dividends and capital
           gains for tax purposes.
 
           When you open your Fund account, you should provide your social
           security or tax identification number on your investment application.
           By providing this information, you will avoid being subject to a
           federal backup withholding tax of 31% on taxable distributions and
           sale proceeds. Any withheld amount would be sent to the IRS as an
           advance tax payment.
 
                                                                              13
<PAGE>
FINANCIAL HIGHLIGHTS
 
The financial highlights table is intended to help you understand the Fund's
financial performance for the past 5 fiscal years of the Fund. Certain
information reflects financial results for a single Fund share. The total
returns in the table represent the rate an investor would have earned or lost on
an investment in the Fund (assuming reinvestment of all dividends and
distributions).
 
This information has been audited by PricewaterhouseCoopers LLP, whose report,
along with the Fund's financial statements, is included in this PROSPECTUS.
 
<TABLE>
<CAPTION>
 YEARS ENDED JANUARY 31                                        1999    1998    1997    1996    1995
<S>                                                           <C>     <C>     <C>     <C>     <C>
- ----------------------------------------------------------------------------------------------------
 
 SELECTED PER-SHARE DATA
- ----------------------------------------------------------------------------------------------------
 Net asset value, beginning of period                         $ 1.00  $ 1.00  $ 1.00  $ 1.00  $ 1.00
                                                              ------  ------  ------  ------  ------
    Net investment income                                      0.045   0.046   0.043   0.049   0.034
- ----------------------------------------------------------------------------------------------------
 LESS DIVIDENDS
    Net investment income                                     (0.045) (0.046) (0.043) (0.049) (0.034)
- ----------------------------------------------------------------------------------------------------
 Net asset value, end of period                               $ 1.00  $ 1.00  $ 1.00  $ 1.00  $ 1.00
- ----------------------------------------------------------------------------------------------------
 
 Total Return                                                   4.63%   4.67%   4.41%   5.00%   3.47%
- ----------------------------------------------------------------------------------------------------
 
 RATIOS TO AVERAGE NET ASSETS
- ----------------------------------------------------------------------------------------------------
 Expenses                                                       0.94%   1.02%   1.11%   1.09%   1.08%
- ----------------------------------------------------------------------------------------------------
 Net investment income                                          4.50%   4.53%   4.29%   4.86%   3.38%
- ----------------------------------------------------------------------------------------------------
 
 SUPPLEMENTAL DATA
- ----------------------------------------------------------------------------------------------------
 Net assets, end of period, in millions                       $1,017  $  891  $  927  $  903  $  809
- ----------------------------------------------------------------------------------------------------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
 
14
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
PORTFOLIO OF INVESTMENTS JANUARY 31, 1999
 
<TABLE>
<CAPTION>
                                                                                ANNUALIZED
PRINCIPAL                           DESCRIPTION                                    YIELD
AMOUNT IN                               AND                                     ON DATE OF
THOUSANDS                          MATURITY DATE                                 PURCHASE             VALUE
- ----------------------------------------------------------------------------------------------------------------
<C>        <S>                                                             <C>                    <C>
           U.S. GOVERNMENT AGENCIES (99.8%)
$126,717   Federal Farm Credit Bank
             02/05/99-07/08/99...........................................       4.72-5.52%        $  125,600,113
 451,331   Federal Home Loan Banks
             02/01/99-07/09/99...........................................        4.62-5.50           448,400,160
 261,524   Federal Home Loan Mortgage Corp. 02/16/99-06/18/99............        4.68-5.10           259,511,674
 173,221   Federal National Mortgage Assoc. 02/02/99-06/10/99............        4.72-5.06           171,818,926
  10,000   Tennessee Valley Authority 03/22/99...........................          4.81                9,932,567
                                                                                                  --------------
 
           TOTAL U.S. GOVERNMENT AGENCIES
           (AMORTIZED COST $1,015,263,440)......................................................   1,015,263,440
                                                                                                  --------------
 
           U.S. GOVERNMENT OBLIGATION (0.7%)
   7,000   U.S. Treasury Bill 03/04/99
             (AMORTIZED COST $6,968,205).................................          5.09                6,968,205
                                                                                                  --------------
 
           REPURCHASE AGREEMENT (0.2%)
   2,085   The Bank of New York due 02/01/99 (dated 01/29/99; proceeds
             $2,085,454) (a) (IDENTIFIED COST $2,084,639)................          4.688               2,084,639
                                                                                                  --------------
</TABLE>
 
<TABLE>
<S>                                                                                       <C>     <C>
TOTAL INVESTMENTS
(IDENTIFIED COST $1,024,316,284) (B)....................................................  100.7 %   1,024,316,284
 
LIABILITIES IN EXCESS OF CASH AND OTHER ASSETS..........................................   (0.7)       (6,851,521)
                                                                                          ------  ---------------
 
NET ASSETS..............................................................................  100.0 % $ 1,017,464,763
                                                                                          ------  ---------------
                                                                                          ------  ---------------
</TABLE>
 
- ---------------------
 
(a)  Collateralized by $1,748,626 U.S. Treasury Bond 6.625% due 02/15/27 valued
     at $2,126,332.
(b)  Cost is the same for federal income tax purposes.
 
                       SEE NOTES TO FINANCIAL STATEMENTS
 
                                                                              15
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS
 
STATEMENT OF ASSETS AND LIABILITIES
JANUARY 31, 1999
 
<TABLE>
<S>                                                                                           <C>
ASSETS:
Investments in securities, at value
  (identified cost $1,024,316,284)..........................................................  $1,024,316,284
Cash........................................................................................          90,001
Receivable for shares of beneficial interest sold...........................................         328,520
Prepaid expenses and other assets...........................................................          36,226
                                                                                              --------------
 
     TOTAL ASSETS...........................................................................   1,024,771,031
                                                                                              --------------
 
LIABILITIES:
Payable for:
    Shares of beneficial interest repurchased...............................................       6,555,859
    Investment management fee...............................................................         354,608
    Plan of distribution fee................................................................          78,679
Accrued expenses............................................................................         317,122
                                                                                              --------------
 
     TOTAL LIABILITIES......................................................................       7,306,268
                                                                                              --------------
 
     NET ASSETS.............................................................................  $1,017,464,763
                                                                                              --------------
                                                                                              --------------
 
COMPOSITION OF NET ASSETS:
Paid-in-capital.............................................................................  $1,017,463,124
Accumulated undistributed net investment income.............................................           1,639
                                                                                              --------------
 
     NET ASSETS.............................................................................  $1,017,464,763
                                                                                              --------------
                                                                                              --------------
 
NET ASSET VALUE PER SHARE,
  1,017,463,124 SHARES OUTSTANDING (UNLIMITED SHARES AUTHORIZED OF $.01 PAR VALUE)..........           $1.00
                                                                                              --------------
                                                                                              --------------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
 
16
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS, CONTINUED
 
STATEMENT OF OPERATIONS
FOR THE YEAR ENDED JANUARY 31, 1999
 
<TABLE>
<S>                                                                                              <C>
NET INVESTMENT INCOME:
 
INTEREST INCOME................................................................................  $50,615,622
                                                                                                 -----------
 
EXPENSES
Investment management fee......................................................................    4,236,205
Transfer agent fees and expenses...............................................................    3,029,492
Plan of distribution fee.......................................................................      903,926
Registration fees..............................................................................      243,033
Shareholder reports and notices................................................................      213,606
Custodian fees.................................................................................       59,794
Professional fees..............................................................................       52,052
Trustees' fees and expenses....................................................................       17,114
Other..........................................................................................       11,421
                                                                                                 -----------
 
     TOTAL EXPENSES............................................................................    8,766,643
                                                                                                 -----------
 
     NET INVESTMENT INCOME.....................................................................   41,848,979
 
     NET REALIZED GAIN.........................................................................       40,360
                                                                                                 -----------
 
NET INCREASE...................................................................................  $41,889,339
                                                                                                 -----------
                                                                                                 -----------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
 
                                                                              17
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS, CONTINUED
 
STATEMENT OF CHANGES IN NET ASSETS
 
<TABLE>
<CAPTION>
                                                                            FOR THE YEAR      FOR THE YEAR
                                                                               ENDED             ENDED
                                                                          JANUARY 31, 1999  JANUARY 31, 1998
- ------------------------------------------------------------------------------------------------------------
<S>                                                                       <C>               <C>
 
INCREASE (DECREASE) IN NET ASSETS:
 
OPERATIONS:
Net investment income...................................................  $     41,848,979  $     40,709,335
Net realized gain.......................................................            40,360         --
                                                                          ----------------  ----------------
 
     NET INCREASE.......................................................        41,889,339        40,709,335
                                                                          ----------------  ----------------
 
DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS FROM:
Net investment income...................................................       (41,849,500)      (40,709,121)
Net realized gain.......................................................           (40,360)        --
                                                                          ----------------  ----------------
 
     TOTAL DIVIDENDS AND DISTRIBUTIONS..................................       (41,889,860)      (40,709,121)
                                                                          ----------------  ----------------
Net increase (decrease) from transactions in shares of beneficial
  interest..............................................................       126,893,998       (36,513,549)
                                                                          ----------------  ----------------
 
     NET INCREASE (DECREASE)............................................       126,893,477       (36,513,335)
 
NET ASSETS:
Beginning of period.....................................................       890,571,286       927,084,621
                                                                          ----------------  ----------------
 
     END OF PERIOD
    (INCLUDING UNDISTRIBUTED NET INVESTMENT INCOME OF $1,639 AND $2,160,
    RESPECTIVELY).......................................................  $  1,017,464,763  $    890,571,286
                                                                          ----------------  ----------------
                                                                          ----------------  ----------------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
 
18
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS JANUARY 31, 1999
 
1. ORGANIZATION AND ACCOUNTING POLICIES
 
Morgan Stanley Dean Witter U.S. Government Money Market Trust (the "Trust"),
formerly Dean Witter U.S. Government Money Market Trust, is registered under the
Investment Company Act of 1940, as amended (the "Act"), as a diversified,
open-end management investment company. The Trust's investment objectives are
security of principal, high current income and liquidity. The Trust was
organized as a Massachusetts business trust on November 18, 1981 and commenced
operations on February 17, 1982.
 
The preparation of financial statements in accordance with generally accepted
accounting principles requires management to make estimates and assumptions that
affect the reported amounts and disclosures. Actual results could differ from
those estimates.
 
The following is a summary of significant accounting policies:
 
A. VALUATION OF INVESTMENTS -- Portfolio securities are valued at amortized
cost, which approximates market value.
 
B. ACCOUNTING FOR INVESTMENTS -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Premiums are amortized and discounts are accreted over the life of the
respective securities.
 
C. FEDERAL INCOME TAX STATUS -- It is the Trust's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute all of its taxable income to its shareholders.
Accordingly, no federal income tax provision is required.
 
D. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS -- The Trust records dividends
and distributions as of the close of each business day.
 
2. INVESTMENT MANAGEMENT AGREEMENT
 
Pursuant to an Investment Management Agreement with Morgan Stanley Dean Witter
Advisors Inc. (the "Investment Manager"), formerly Dean Witter InterCapital
Inc., the Trust pays the Investment Manager a management fee, accrued daily and
payable monthly, by applying the following annual rates to the net assets of the
Trust determined as of the close of each business day: 0.50% to the portion of
the daily net assets not exceeding $500 million; 0.425% to the portion of the
daily net assets exceeding $500 million but not exceeding $750 million; 0.375%
to the portion of the daily net
 
                                                                              19
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS JANUARY 31, 1999, CONTINUED
 
assets exceeding $750 million but not exceeding $1 billion; 0.35% to the portion
of the daily net assets exceeding $1 billion but not exceeding $1.5 billion;
0.325% to the portion of the daily net assets exceeding $1.5 billion but not
exceeding $2 billion; 0.30% to the portion of the daily net assets exceeding $2
billion but not exceeding $2.5 billion; 0.275% to the portion of the daily net
assets exceeding $2.5 billion but not exceeding $3 billion; and 0.25% to the
portion of the daily net assets exceeding $3 billion.
 
Under the terms of the Agreement, the Investment Manager maintains certain of
the Trust's books and records and furnishes, at its own expense, office space,
facilities, equipment, clerical, bookkeeping and certain legal services and pays
the salaries of all personnel, including officers of the Trust who are employees
of the Investment Manager. The Investment Manager also bears the cost of
telephone services, heat, light, power and other utilities provided to the
Trust.
 
3. PLAN OF DISTRIBUTION
 
Morgan Stanley Dean Witter Distributors Inc. (the "Distributor"), an affiliate
of the Investment Manager, is the distributor of the Trust's shares and, in
accordance with a Plan of Distribution (the "Plan") pursuant to Rule 12b-1 under
the Act, finances certain expenses in connection therewith.
 
Under the Plan, the Distributor bears the expense of all promotional and
distribution related activities on behalf of the Trust, except for expenses that
the Trustees determine to reimburse, as described below. The following
activities and services may be provided by the Distributor, and other selected
broker-dealers under the Plan: (1) compensation to, and expenses of, Morgan
Stanley Dean Witter Financial Advisors and other selected broker-dealers; (2)
sales incentives and bonuses to sales representatives and to marketing personnel
in connection with promoting sales of the Trust's shares; (3) expenses incurred
in connection with promoting sales of the Trust's shares; (4) preparing and
distributing sales literature; and (5) providing advertising and promotional
activities, including direct mail solicitation and television, radio, newspaper,
magazine and other media advertisements.
 
The Trust is authorized to reimburse the Distributor for specific expenses the
Distributor incurs or plans to incur in promoting the distribution of the
Trust's shares. The amount of each monthly reimbursement payment may in no event
exceed an amount equal to a payment at the annual rate of 0.15% of the Trust's
average daily net assets during the month. Expenses incurred by the Distributor
pursuant to the Plan in any fiscal year will not be reimbursed by the Trust
through payments accrued in any subsequent fiscal year. For the year ended
January 31, 1999, the distribution fee was accrued at the annual rate of 0.10%.
 
20
<PAGE>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS JANUARY 31, 1999, CONTINUED
 
4. SECURITY TRANSACTIONS AND TRANSACTIONS WITH AFFILIATES
 
The cost of purchases and proceeds from sales/maturities of portfolio securities
for the year ended January 31, 1999 aggregated $12,774,924,363 and
$12,697,076,883, respectively.
 
Morgan Stanley Dean Witter Trust FSB, an affiliate of the Investment Manager and
Distributor, is the Trust's transfer agent. At January 31, 1999, the Trust had
transfer agent fees and expenses payable of approximately $152,800.
 
The Trust has an unfunded noncontributory defined benefit pension plan covering
all independent Trustees of the Trust who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on years of service and compensation during the last five years
of service. Aggregate pension costs for the year ended January 31, 1999 included
in Trustees' fees and expenses in the Statement of Operations amounted to
$6,203. At January 31, 1999, the Trust had an accrued pension liability of
$50,731 which is included in accrued expenses in the Statement of Assets and
Liabilities.
 
5. SHARES OF BENEFICIAL INTEREST
 
Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:
 
<TABLE>
<CAPTION>
                                                                     FOR THE YEAR        FOR THE YEAR
                                                                         ENDED               ENDED
                                                                   JANUARY 31, 1999    JANUARY 31, 1998
                                                                   -----------------   -----------------
<S>                                                                <C>                 <C>
Shares sold......................................................      2,239,344,299       2,013,452,444
Shares issued in reinvestment of dividends.......................         41,717,140          40,560,689
Acquisition of Dean Witter Retirement Series -- U.S. Government
 Money Market....................................................            837,211          --
                                                                   -----------------   -----------------
                                                                       2,281,898,650       2,054,013,133
Shares repurchased...............................................     (2,155,004,652)     (2,090,526,682)
                                                                   -----------------   -----------------
Net increase (decrease)..........................................        126,893,998         (36,513,549)
                                                                   -----------------   -----------------
                                                                   -----------------   -----------------
</TABLE>
 
6. ACQUISITION OF DEAN WITTER RETIREMENT SERIES -- U.S. GOVERNMENT MONEY MARKET
SERIES
 
As of the close of business on September 11, 1998, the Trust acquired all the
net assets of Dean Witter Retirement Series -- U.S. Government Money Market
Series ("Retirement U.S. Government") pursuant to a plan of reorganization
approved by shareholders of Retirement U.S. Government on August 19, 1998. The
acquisition was accomplished by a tax-free exchange of 837,211 shares of the
Trust at a net asset value of $1.00 per share for 837,211 shares of Retirement
U.S. Government. The net assets of the Trust and Retirement U.S. Government
immediately before the acquisition were $942,511,862 and $837,211, respectively.
Immediately after the acquisition, the combined net assets of the Trust amounted
to $943,349,073.
 
                                                                              21
<PAGE>
 
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT
MONEY MARKET TRUST
REPORT OF INDEPENDENT ACCOUNTANTS
 
TO THE SHAREHOLDERS AND TRUSTEES
OF MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
 
In our opinion, the accompanying statement of assets and liabilities, including
the portfolio of investments, and the related statements of operations and of
changes in net assets and the financial highlights (appearing in the "Financial
Highlights" table on page 14 of this Prospectus) present fairly, in all material
respects, the financial position of Morgan Stanley Dean Witter U.S. Government
Money Market Trust (the "Trust") formerly Dean Witter U.S. Government Money
Market Trust, at January 31, 1999, the results of its operations for the year
then ended, the changes in its net assets for each of the two years in the
period then ended and the financial highlights for each of the five years in the
period then ended, in conformity with generally accepted accounting principles.
These financial statements and financial highlights (hereafter referred to as
"financial statements") are the responsibility of the Trust's management; our
responsibility is to express an opinion on these financial statements based on
our audits. We conducted our audits of these financial statements in accordance
with generally accepted auditing standards which require that we plan and
perform the audit to obtain reasonable assurance about whether the financial
statements are free of material misstatement. An audit includes examining, on a
test basis, evidence supporting the amounts and disclosures in the financial
statements, assessing the accounting principles used and significant estimates
made by management, and evaluating the overall financial statement presentation.
We believe that our audits, which included confirmation of securities at January
31, 1999 by correspondence with the custodian, provide a reasonable basis for
the opinion expressed above.
 
Pricewaterhouse Coopers LLP
1177 AVENUE OF THE AMERICAS
NEW YORK, NEW YORK 10036
MARCH 5, 1999
 
22
<PAGE>
 
  2  3  0 --
 for office use only
 
                                                                [LOGO]
APPLICATION
 
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
Send to: Morgan Stanley Dean Witter Trust FSB (the "Transfer Agent"), P.O. Box
1040, Jersey City, NJ 07303
 
<TABLE>
<S>             <C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C>
INSTRUCTIONS    For assistance in completing this application, telephone Morgan Stanley Dean Witter Trust FSB at (800) 869-NEWS
                (toll-free).
TO REGISTER
SHARES          1.[REMOVE APPLICATION CAREFULLY]
(please print)
                ---------------------------------------------------------------------------------------------------------------
                                  First Name                                    Last Name
- -As joint
  tenants,
  use line 1 & 2  2.
                ---------------------------------------------------------------------------------------------------------------
                                  First Name                                    Last Name
                   (Joint tenants with rights of survivorship unless otherwise
                   specified)
                                                                                              ------------------------
</TABLE>
<TABLE>
<S>             <C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C><C>
                                                                                              Social Security Number
- -As custodian
  for a minor,   3.
  use lines 1 &
  3
                ---------------------------------------------------------------------------------------------------------------
                                                                    Minor's Name
                   Under the________Uniform Gifts to Minors Act                            ---------------------------
                                                                                           Minor's Social Security Number
                   State of Residence of Minor
- -In the name of a
  corporation,   4.
  trust,
  partnership
  or other      ---------------------------------------------------------------------------------------------------------------
                                    Name of Corporation, Trust (including trustee name(s)) or Other Organization
  institutional
  investors, use
  line 4
                   If Trust, Date of Trust Instrument:____________                          Tax Identification
                                                                                             Number__________
ADDRESS
                ---------------------------------------------------------------------------------------------------------------
                   City                       State                       Zip Code
</TABLE>
 
<TABLE>
<S>               <C>                                                                                                            <C>
TO PURCHASE
SHARES:
Minimum Initial   / / CHECK (enclosed) $__________ (Make Payable to Morgan Stanley Dean Witter U.S. Government Money Market
Investment:       Trust)
$1,000            / / WIRE*  On__________          MF*________
                  (Date)                            (Control number, this transaction)
</TABLE>
 
<TABLE>
<S>               <C>                                                                                                         <C>
                  ----------------------------------------------------------------------------------------------------------
                  Name of Bank                                                                        Branch
                  ----------------------------------------------------------------------------------------------------------
                  Address
                  ----------------------------------------------------------------------------------------------------------
                  Telephone Number
                  * For an initial investment made by wiring funds, obtain a control number by calling: (800) 869-NEWS
                  (toll-free).
                   Your bank should wire to:
                  Bank of New York for credit to account of Morgan Stanley Dean Witter Trust FSB
</TABLE>
 
<TABLE>
<S>               <C>                                                                                                         <C>
                  Account Number: 8900188413
                  Re: Morgan Stanley Dean Witter U.S. Government Money Market Trust
                  Account Of:______________________
                  (Investor's Account as Registered at the Transfer Agent)
                  Control or Account Number:______________________
                  (Assigned by Telephone)
                                                         OPTIONAL SERVICES
</TABLE>
 
<TABLE>
<S>               <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>  <C>
                  NOTE: If you are a current shareholder of Morgan Stanley Dean Witter
                  U.S. Government Money Market Trust, please indicate your fund
                  account number here.
                  [ 2 ] [ 3 ] [ 0 ]  -
</TABLE>
 
<TABLE>
<S>               <C>
DIVIDENDS         All dividends will be reinvested daily in additional shares, unless the following option is selected:
                  / / Pay income dividends by check at the end of each month.
WRITE YOUR OWN    / / Send an initial supply of checks.
CHECK             FOR JOINT ACCOUNTS:
                  / / CHECK THIS BOX IF ALL OWNERS ARE REQUIRED TO SIGN CHECKS.
</TABLE>
 
<PAGE>
 
<TABLE>
<S>               <C>                                                                              <C>                           <C>
                  / /  Morgan Stanley Dean Witter Trust FSB is hereby authorized to honor telephonic or other instructions, without
PAYMENT TO           signature guarantee, from any person for the redemption of any or all shares of Morgan Stanley Dean Witter U.S.
PREDESIGNATED          Government Money Market Trust held in my (our) account provided that proceeds are transmitted only to the
BANK ACCOUNT           following bank account. (Absent its own negligence, neither Morgan Stanley Dean Witter U.S. Government Money
                       Market Trust nor Morgan Stanley Dean Witter Trust FSB (the "Transfer Agent") shall be liable for any
                       redemption caused by unauthorized instruction(s)):
Bank Account must be in
same  name  as  shares  are
registered        -------------------------------------------------------------------------------  ------------------------------
                  NAME & BANK ACCOUNT NUMBER                                                        BANK'S ROUTING TRANSMIT CODE
                                                                                                          (ASK YOUR BANK)
Minimum Amount:
$1,000            NAME OF BANK
                  -------------------------------------------------------------------------------
                  ADDRESS OF BANK
                  -------------------------------------------------------------------------------
                  TELEPHONE NUMBER OF BANK
                                                              SIGNATURE AUTHORIZATION
FOR ALL ACCOUNTS  NOTE: RETAIN A COPY OF THIS DOCUMENT FOR YOUR RECORDS. ANY MODIFICATION OF THE INFORMATION BELOW WILL REQUIRE AN
                  AMENDMENT TO THIS FORM. THIS DOCUMENT IS IN FULL FORCE AND EFFECT UNTIL ANOTHER DULY EXECUTED FORM IS RECEIVED BY
                  THE TRANSFER AGENT.
                  The "Transfer Agent" is hereby authorized to act as agent for the registered owner of shares of Morgan Stanley
                  Dean Witter U.S. Government Money Market Trust (the "Fund") in effecting redemptions of shares and is authorized
                  to recognize the signature(s) below in payment of funds resulting from such redemptions on behalf of the
                  registered owners of such shares. The Transfer Agent shall be liable only for its own negligence and not for
                  default or negligence of its correspondents, or for losses in transit. The Fund shall not be liable for any
                  default or negligence of the Transfer Agent.
                  I (we) certify to my (our) legal capacity, or the capacity of the investor named above, to invest in and redeem
                  shares of, and I (we) acknowledge receipt of a current prospectus of, Morgan Stanley Dean Witter U.S. Government
                  Money Market Trust and (we) further certify my (our) authority to sign and act for and on behalf of the investor.
                  Under penalties of perjury, I certify (1) that the number shown on this form is my correct taxpayer identification
                  number and (2) that I am not subject to backup withholding either because I have not been notified that I am
                  subject to backup withholding as a result of a failure to report all interest or dividends, or the Internal
                  Revenue Service has notified me that I am no longer subject to backup withholding. (Note: You must cross out item
                  (2) above if you have been notified by IRS that you are currently subject to backup withholding because of
                  underreporting interest or dividends on your tax return.)
                  For Individual, Joint and Custodial Accounts for Minors, Check Applicable Box:
                  / / I am a United States Citizen.                     / / I am not a United States Citizen.
                                                  SIGNATURE(S) (IF JOINT TENANTS, ALL MUST SIGN)
</TABLE>
 
<TABLE>
<S>               <C>                                                       <C>
                  ------------------------------------------------          ------------------------------------------------
                          SIGNATURE MUST BE KEPT WITHIN ABOVE AREA                  SIGNATURE MUST BE KEPT WITHIN ABOVE AREA
                  --------------------------------------------------------  --------------------------------------------------------
                          SIGNATURE MUST BE KEPT WITHIN ABOVE AREA                  SIGNATURE MUST BE KEPT WITHIN ABOVE AREA
Name(s) must be
signed
exactly the same  SIGNED THIS_______________DAY OF__________, 19____.
as shown on
lines 1 to 4 on
the reverse
side of this                                FOR CORPORATIONS, TRUSTS, PARTNERSHIPS AND OTHER ORGANIZATIONS
application
                  The following named persons are currently officers/trustees/general partners/other authorized signatories of the
                  Registered Owner, and any * of them ("Authorized Person(s)") is/are currently authorized under the applicable
                  governing document to act with full power to sell, assign or transfer securities of the the Fund for the
                  Registered Owner and to execute and deliver any instrument necessary to effectuate the authority hereby conferred:
                                         NAME/TITLE                                                SIGNATURE
</TABLE>
 
<TABLE>
<S>               <C>                                                       <C>
In addition,
complete
Section A or B    --------------------------------------------------------  --------------------------------------------------------
below.
                  --------------------------------------------------------  --------------------------------------------------------
                          SIGNATURE MUST BE KEPT WITHIN ABOVE AREA                  SIGNATURE MUST BE KEPT WITHIN ABOVE AREA
                  --------------------------------------------------------  --------------------------------------------------------
                          SIGNATURE MUST BE KEPT WITHIN ABOVE AREA                  SIGNATURE MUST BE KEPT WITHIN ABOVE AREA
                  --------------------------------------------------------  --------------------------------------------------------
                          SIGNATURE MUST BE KEPT WITHIN ABOVE AREA                  SIGNATURE MUST BE KEPT WITHIN ABOVE AREA
                  SIGNED THIS____________DAY OF____________, 19____.
                  The Transfer Agent may, without inquiry, act only upon the instruction of ANY PERSON(S) purporting to be (an)
                  Authorized Person(s) as named in the Certification Form last received by the Transfer Agent. The Transfer Agent
                  and the Fund shall not be liable for any claims, expenses (including legal fees) or losses resulting from the
                  Transfer Agent having acted upon any instruction reasonably believed genuine.
                  ------------------------------------------------------------------------------------------------------------------
                  *INSERT A NUMBER. UNLESS OTHERWISE INDICATED, THE TRANSFER AGENT MAY HONOR INSTRUCTIONS OF ANY ONE OF THE PERSONS
                   NAMED ABOVE.
</TABLE>
 
<TABLE>
<S>                   <C>
SECTION (A)           NOTE: EITHER A SIGNATURE GUARANTEE OR CORPORATE SEAL IS REQUIRED.
CORPORATIONS AND
INCORPORATED
ASSOCIATIONS ONLY.    I, ____________, Secretary of the Registered Owner, do hereby certify that at a meeting on
SIGN ABOVE AND COM-   ____________ at which a quorum was present throughout, the Board of Directors of the
PLETE THIS            corporation/the officers of the association duly adopted a resolution, which is in full force and
SECTION               effect and in accordance with the Registered Owner's charter and by-laws, which resolution did the
                      following: (1) empowered the above-named Authorized Person(s) to effect securities transactions
                      for the Registered Owner on the terms described above; (2) authorized the Secretary to certify,
                      from time to time, the names and titles of the officers of the Registered Owner and to notify the
                      Transfer Agent when changes in office occur; and (3) authorized the Secretary to certify that such
                      a resolution has been duly adopted and will remain in full force and effect until the Transfer
                      Agent receives a duly executed amendment to the Certification Form.
SIGNATURE
GUARANTEE**           Witness my hand on behalf of the corporation/association this ______ day of ____________, 19____.
(or Corporate Seal)
                      --------------------------------------------------------------------------------------------------
                                                                 Secretary**
                      The undersigned officer (other than the Secretary) hereby certifies that the foregoing instrument
                      has been signed by the Secretary of the
                      corporation/association.
SIGNATURE
GUARANTEE**           --------------------------------------------------------------------------------------------------
(or Corporate Seal)                  Certifying Officer of the Corporation or Incorporated Association**
SECTION (B) ALL                                    NOTE: A SIGNATURE GUARANTEE IS REQUIRED.
OTHER
INSTITUTIONAL         --------------------------------------------------------------------------------------------------
INVESTORS                                                         Certifying
SIGNATURE                                          Trustee(s)/General Partner(s)/Other(s)**
GUARANTEE**
                      --------------------------------------------------------------------------------------------------
SIGN ABOVE AND COM-                                               Certifying
PLETE THIS SECTION                                 Trustee(s)/General Partner(s)/Other(s)**
                      **SIGNATURE(S) MUST BE GUARANTEED BY AN ELIBIGLE GUARANTOR
</TABLE>
 
<TABLE>
<S>               <C>                                                   <C>                                                 <C>
DEALER            Above signature(s) guaranteed. Prospectus has been delivered by undersigned to above-named applicant(s).
(if any)
Completion by
dealer only       ----------------------------------------------------  ----------------------------------------------------
                  Firm Name                                             Office Number-Account Number at Dealer-A/E Number
                  ----------------------------------------------------  ----------------------------------------------------
                  Address                                               Account Executive's Last Name
                  ----------------------------------------------------  ----------------------------------------------------
                  City, State, Zip Code                                 Branch Office
</TABLE>
 
- -Registered Trademark- 1999 Morgan Stanley Dean Witter Distributors Inc.
<PAGE>
MORGAN STANLEY DEAN WITTER
FAMILY OF FUNDS
 
                           The Morgan Stanley Dean Witter Family of Funds offers
                           investors a wide range of investment choices. Come on
                           in and meet the family!
- --------------------------------------------------------------------------------
 GROWTH FUNDS
- ---------------------------------
   
    

Aggressive Equity Fund
American Value Fund
Capital Growth Securities
Developing Growth Securities
Equity Fund
Growth Fund
Market Leader Trust
Mid-Cap Growth Fund
Special Value Fund
Value Fund
 
THEME FUNDS
Financial Services Trust
Health Sciences Trust
Information Fund
Natural Resource Development Securities
Precious Metals and Minerals Trust
 
GLOBAL/INTERNATIONAL FUNDS
Competitive Edge Fund - "Best Ideas" Portfolio
European Growth Fund
Fund of Funds - International Portfolio
Global Dividend Growth Securities
International SmallCap Fund
Japan Fund
Pacific Growth Fund
- --------------------------------------------------------------------------------
 GROWTH AND INCOME FUNDS
- ---------------------------------
Balanced Growth Fund
Balanced Income Fund
Convertible Securities Trust
Dividend Growth Securities
Fund of Funds - Domestic Portfolio
Income Builder Fund
Mid-Cap Dividend Growth Securities
S&P 500 Index Fund
S&P 500 Select Fund
Strategist Fund
Value-Added Market Series/Equity Portfolio
 
THEME FUNDS
Global Utilities Fund
Real Estate Fund
Utilities Fund
- --------------------------------------------------------------------------------
 INCOME FUNDS
- ---------------------------------
 
GOVERNMENT INCOME FUNDS
Federal Securities Trust
Short-Term U.S. Treasury Trust
U.S. Government Securities Trust
 
DIVERSIFIED INCOME FUNDS
Diversified Income Trust
 
CORPORATE INCOME FUNDS
High Yield Securities
Intermediate Income Securities
Short-Term Bond Fund (NL)
 
GLOBAL INCOME FUNDS
World Wide Income Trust
 
TAX-FREE INCOME FUNDS
California Tax-Free Income Fund
Hawaii Municipal Trust (FSC)
Limited Term Municipal Trust (NL)
Multi-State Municipal Series Trust (FSC)
New York Tax-Free Income Fund
Tax-Exempt Securities Trust
- --------------------------------------------------------------------------------
 MONEY MARKET FUNDS
- ---------------------------------
 
TAXABLE MONEY MARKET FUNDS
Liquid Asset Fund (MM)
U.S. Government Money Market Trust (MM)
 
TAX-FREE MONEY MARKET FUNDS
California Tax-Free Daily Income Trust (MM)
N.Y. Municipal Money Market Trust (MM)
Tax-Free Daily Income Trust (MM)
 
There may be Funds created after this PROSPECTUS was published. Please consult
the inside front cover of a new Fund's PROSPECTUS for its designation, e.g.,
Multi-Class Fund or Money Market Fund.
 
Unless otherwise noted, each listed Morgan Stanley Dean Witter Fund, except for
Short-Term U.S. Treasury Trust, is a Multi-Class Fund. A Multi-Class Fund is a
mutual fund offering multiple Classes of shares. The other types of funds are:
NL - No-Load (Mutual) Fund; MM - Money Market Fund; FSC - A mutual fund sold
with a front-end sales charge and a distribution (12b-1) fee.
<PAGE>
                                                     PROSPECTUS - MARCH 29, 1999
 
Additional information about the Fund's investments is available in the Fund's
ANNUAL AND SEMI-ANNUAL REPORTS TO SHAREHOLDERS (the current annual report is
included in this PROSPECTUS). The Fund's STATEMENT OF ADDITIONAL INFORMATION
also provides additional information about the Fund. The STATEMENT OF ADDITIONAL
INFORMATION is incorporated herein by reference (legally is part of this
PROSPECTUS). For a free copy of any of these documents, to request other
information about the Fund, or to make shareholder inquiries, please call:
 
                                 (800) 869-NEWS
 
You also may obtain information about the Fund by calling your Morgan Stanley
Dean Witter Financial Advisor or by visiting our Internet site at:
                            www.deanwitter.com/funds
 
Information about the Fund (including the STATEMENT OF ADDITIONAL INFORMATION)
can be viewed and copied at the Securities and Exchange Commission's Public
Reference Room in Washington, DC. Information about the Reference Room's
operations may be obtained by calling the SEC at (800) SEC-0330. Reports and
other information about the Fund are available on the SEC's Internet site
(www.sec.gov) and copies of this information may be obtained, upon payment of a
duplicating fee, by writing the Public Reference Section of the SEC, Washington,
DC 20549-6009.
 
Morgan Stanley Dean Witter
                                                                 U.S. GOVERNMENT
                                                              MONEY MARKET TRUST
 
                               [BACK COVER PHOTO]
 
 TICKER SYMBOL: DWGXX
 
(INVESTMENT COMPANY ACT FILE NO. 811-3326)
<PAGE>
   
           A MONEY MARKET FUND THAT SEEKS TO PROVIDE SECURITY OF PRINCIPAL, HIGH
                                                    CURRENT INCOME AND LIQUIDITY
    


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