<PAGE>   1
 
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------
 
                                  FORM 10-K/A
                                AMENDMENT NO. 1
                            ------------------------
 
(MARK ONE)
 
     [X]   ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
           EXCHANGE ACT OF 1934
 
                  FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998
 
                                       OR
 
     [ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
           EXCHANGE ACT OF 1934
 
       FOR THE TRANSITION PERIOD FROM                TO                 .
 
                         COMMISSION FILE NUMBER 0-22712
 
                          VERITAS SOFTWARE CORPORATION
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                       <C>
                DELAWARE                                 94-2823068
    (STATE OR OTHER JURISDICTION OF         (I.R.S. EMPLOYER IDENTIFICATION NO.)
     INCORPORATION OR ORGANIZATION)
 
          1600 PLYMOUTH STREET
       MOUNTAIN VIEW, CALIFORNIA                           94043
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                 (ZIP CODE)
</TABLE>
 
       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (650) 335-8000
 
     SECURITIES TO BE REGISTERED PURSUANT TO SECTION 12(B) OF THE ACT: NONE
 
 SECURITIES TO BE REGISTERED PURSUANT TO SECTION 12(G) OF THE ACT: COMMON STOCK
 
     Indicate by check mark whether the registrant: (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]
 
     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K.  [X]
 
     As of February 28, 1999, 47,924,510 shares of registrant's common stock
were outstanding. The aggregate market value of the common stock held by
non-affiliates of the registrant as of February 28, 1999 was approximately
$2,833,634,700.
 
                      DOCUMENTS INCORPORATED BY REFERENCE
                                      None
 
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<PAGE>   2
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                                      PAGE NO.
                                                                      --------
<S>     <C>                                                           <C>
                                   PART III
Item
  10.   Directors and Executive Officers of the Registrant..........      3
Item
  11.   Executive Compensation......................................      5
Item
  12.   Security Ownership of Certain Beneficial Owners and               7
          Management................................................
Item
  13.   Certain Relationships and Related Transactions..............      8
 
Signatures..........................................................      9
</TABLE>
 
                                        2
<PAGE>   3
 
                                    PART III
 
ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT
 
DIRECTORS
 
     The following table sets forth information as of March 31, 1999 with
respect to persons who are members of the Board of Directors of VERITAS Software
Corporation:
 
<TABLE>
<CAPTION>
          NAME             AGE                        TITLE
          ----             ---                        -----
<S>                        <C>   <C>
Mark Leslie                53    Chief Executive Officer and Chairman of the
                                 Board
Geoffrey W. Squire         52    Executive Vice-President and Vice-Chairman of
                                 the Board
Fred van den Bosch         52    Executive Vice President of Engineering,
                                 Director
Steven Brooks              47    Director
William H. Janeway         55    Director
Joseph D. Rizzi            56    Director
Roel Pieper                42    Director
</TABLE>
 
     Directors will hold office until the next annual meeting of stockholders
and until their successors have been elected and qualified or until their
earlier resignation or removal. Executive officers will be chosen by and will
serve at the discretion of the Board of Directors. There is no family
relationship between any director or executive officer of VERITAS and any other
director or executive officer of VERITAS.
 
     Mr. Leslie has served as President and Chief Executive Officer of VERITAS
since 1990 and as a director of VERITAS since 1988. Prior to 1990, he was the
principal and owner of Leslie Consulting, a management consulting firm and
President and Chief Executive Officer of Rugged Digital Systems, Inc., a
computer manufacturer. Mr. Leslie is also Chairman of the Board of Versant
Object Technology Corporation, an object-oriented database software company.
 
     Mr. Squire has been Co-Chairman of the Board of Directors and Executive
Vice-President of VERITAS since April 1997, when VERITAS merged with OpenVision.
Mr. Squire became a director of OpenVision in January 1994 and was appointed
Chief Executive Officer of OpenVision in July 1995. From January 1994 to
November 1994, Mr. Squire was Executive Vice President and Chief Executive
Officer of International Operations and from November 1994 to June 1995, he was
President and Chief Operating Officer of OpenVision. Prior to that time, Mr.
Squire worked at Oracle Corporation, most recently as a member of Oracle's
Executive Committee as Chief Executive, International Operations. Mr. Squire has
sat on the Council of the U.K. Computing Services and Software Association since
1990. In 1995, Mr. Squire was elected as the founding President of the European
Information Services Association. Mr. Squire also serves as a director of
Industri-Mathematik International Corp.
 
     Mr. van den Bosch has served as Executive Vice President, Engineering of
VERITAS since July 1997. Mr. van den Bosch served as Senior Vice President,
Engineering of VERITAS from 1991 to July 1997 and was appointed as a director of
VERITAS in February 1996. From 1970 until 1990, he served in various positions
with Philips Information Systems, including Director of Technology.
 
     Mr. Brooks has been a director of VERITAS since April 1996. Since February
1999, Mr. Brooks has been General Partner of Broadview Capital Partners, a
private equity firm.
 
                                        3
<PAGE>   4
 
From September 1997 to February 1999, Mr. Brooks was a managing director of
Donaldson, Lufkin & Jenrette Securities Corporation, an investment banking firm.
From 1996 to 1997, Mr. Brooks was a private investor and a consultant to
technology companies. From 1994 to 1996, Mr. Brooks served as Managing Director
and Head of Global Technology Investment Banking at the Union Bank of
Switzerland Securities, LLC. Prior to 1994, Mr. Brooks was a private investor
and consultant to high-technology firms, and served as Managing Partner of
investment banking at Robertson, Stephens & Co., an investment bank. Mr. Brooks
is a director of Paychex, Inc. a national payroll processing and business
services company, and QRS, an electronic commerce company.
 
     Mr. Janeway has been a director of VERITAS since April 1997. Mr. Janeway
has been a Managing Director of E.M. Warburg Pincus & Co., LLC since 1988. Prior
to 1988, he served in a management capacity at F. Eberstadt & Co., Inc. Mr.
Janeway is a director of ECsoft Group, PLC, Vanstar Corporation, Maxis, Inc.,
Zilog, Inc., and Industri-Mathematik Intl. Corp.
 
     Mr. Rizzi has been a director of VERITAS since 1987. Prior to that date, he
served as a general partner of Matrix Partners, a venture capital firm, and as
Chief Executive Officer of Elxsi, a computer company.
 
     Mr. Pieper has been a director of VERITAS since 1992. Mr. Pieper has served
as Executive Vice President of Philips Electronics, The Netherlands, since
January 1998. From 1996 to January 1999, Mr. Pieper was President and Chief
Executive Officer of Tandem Computers Incorporated, a manufacturer of
fault-tolerant computer systems. From 1993 to 1996 he served as President and
Chief Executive Officer of Ungermann-Bass, Inc., a global data network
integrator and product supplier, and Senior Vice President of Tandem Computers
Incorporated, the parent company of Ungermann-Bass, Inc. From 1991 to 1993, he
served in various executive capacities for UNIX System Laboratories. Mr. Pieper
also serves as a director of General Magic, Inc., Computer Associates, and
Lincoln National Corporation.
 
            SECTION 16(A) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE
 
     In accordance with Section 16(a) of the Securities Exchange Act of 1934, as
amended, and the regulations of the Securities and Exchange Commission, VERITAS'
directors, certain officers, and greater than 10% stockholders are required to
file reports of ownership and changes in ownership with the SEC and the Nasdaq
National Market and to furnish VERITAS with copies of all such reports they
file.
 
     Based solely on its review of the copies of such forms furnished to VERITAS
and written representations from certain reporting persons, VERITAS is unaware
of any failures during 1998 to file Forms 3, 4 or 5 or any failures to file such
forms in a timely basis.
 
EXECUTIVE OFFICERS
 
     Information with respect to executive officers may be found in Item 1.
Business.
 
                                        4
<PAGE>   5
 
ITEM 11. EXECUTIVE COMPENSATION
 
COMPENSATION OF EXECUTIVE OFFICERS
 
     The following table sets forth all compensation awarded to, earned by or
paid for services rendered to VERITAS Software Corporation in all capacities
during 1996, 1997 and 1998 by VERITAS' chief executive officer and VERITAS' four
other most highly compensated executive officers. This information includes the
dollar value of base salaries, commissions and bonus awards, the number of
shares subject to stock options granted and certain other compensation, whether
paid or deferred. VERITAS does not grant stock appreciation rights and has no
long-term compensation benefits other than stock options.
 
                           SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                                                                        LONG-TERM
                                                                                       COMPENSATION
                                                                                       ------------
                                                          ANNUAL COMPENSATION             AWARDS
                                                   ---------------------------------    SECURITIES
                                                                     OTHER ANNUAL       UNDERLYING
NAME AND PRINCIPAL POSITION   YEAR    SALARY($)      BONUS($)       COMPENSATION($)     OPTIONS(#)
---------------------------   ----   -----------   -------------   -----------------   ------------
<S>                           <C>    <C>           <C>             <C>                 <C>
Mark Leslie.................  1998   $   300,000     $398,765           $ 1,200          123,750
  President, Chief            1997       250,000      326,400             1,200          191,248
  Executive Officer           1996       230,000      170,800                 0          168,750
Geoffrey W. Squire..........  1998       240,213      236,867                 0           41,250
  Executive Vice President    1997       169,689      208,875            18,444                0
                              1996             0            0                 0                0
Fred van den Bosch..........  1998       220,000      219,321             1,200           82,500
  Executive Vice              1997       160,000      140,598             1,200          112,498
  President of Engineering    1996       145,000       78,082                 0           50,625
Paul A. Sallaberry..........  1998       300,350       99,691             1,200           37,500
  Senior Vice President,      1997       284,170       58,485             1,200           78,748
  Worldwide Sales             1996             0            0                 0                0
Kenneth E. Lonchar..........  1998       191,200      179,444                 0           22,500
  Chief Financial Officer     1997       114,667      133,680                 0           22,498
  Sr. Vice President,
     Finance                  1996             0            0                 0                0
</TABLE>
 
     Portions of bonuses for services rendered in fiscal year 1996, 1997 and
1998 were each paid in the following year. Share data has been restated to give
retroactive effect to a 3-for-2 stock split in the form of a stock dividend
effected on May 20, 1998. Mr. Sallaberry and Mr. Squire joined VERITAS in April
1997 when VERITAS merged with OpenVision Technologies, Inc. The compensation
amounts include sales commissions paid to Mr. Sallaberry by VERITAS in the
amount of $118,965 in 1996 and $170,837 in 1997.
 
                                        5
<PAGE>   6
 
OPTION GRANTS IN 1998
 
     The following table sets forth further information regarding the individual
grants of stock options pursuant to VERITAS' stock option plans during fiscal
1998 to each of the VERITAS named officers. The table illustrates the
hypothetical gains or "option spreads" that would exist for the options at the
end of the ten-year term of the option based on assumed annualized rates of
compound stock price appreciation of 5% and 10% from the dates the options were
granted to the end of the term. The 5% and 10% assumed rates of annual compound
stock price appreciation are mandated by rules of the Securities and Exchange
Commission and do not represent VERITAS' estimate or projection of future common
stock prices. Actual gains, if any, on option exercises will depend on the
future performance of VERITAS' common stock and overall market conditions. The
potential realizable values shown in this table may never be achieved.
 
<TABLE>
<CAPTION>
                                                                                       POTENTIAL REALIZABLE
                                                                                         VALUE AT ASSUMED
                          NUMBER OF     PERCENT OF                                        ANNUAL RATES OF
                          SECURITIES   TOTAL OPTIONS                                 STOCK PRICE APPRECIATION
                          UNDERLYING    GRANTED TO                                        FOR OPTION TERM
                           OPTIONS     EMPLOYEES IN    EXERCISE PRICE   EXPIRATION   -------------------------
         NAME              GRANTED      FISCAL YEAR       ($/SHR)          DATE          5%            10%
         ----             ----------   -------------   --------------   ----------   -----------   -----------
<S>                       <C>          <C>             <C>              <C>          <C>           <C>
Mark Leslie............    123,750          5.4            $39.17        4/14/08      3,048,176     7,724,677
Geoffrey W. Squire.....     41,250          1.8            $39.17        4/14/08      1,016,059     2,574,892
Fred van den Bosch.....     82,500          3.6            $39.17        4/14/08      2,032,117     5,149,785
Paul A. Sallaberry.....     37,500          1.6            $39.17        4/14/08        923,690     2,340,811
Kenneth E. Lonchar.....     22,500          1.0            $39.17        4/14/08        554,214     1,404,487
</TABLE>
 
     The exercise price of all stock options was equal to the fair market value
of VERITAS' common stock on the date of grant. Stock options vest over four
years at the rate of 1/48 per month, such vesting to accelerate in the event of
an acquisition or merger of VERITAS. The options were granted for a term of ten
years, subject to earlier termination upon termination of employment. Share and
per share data has been restated to give retroactive effect to a 3-for-2 stock
split in the form of a stock dividend in May 1998.
 
AGGREGATE OPTION EXERCISES IN 1998 AND FISCAL YEAR-END OPTION VALUES
 
     The following table sets forth certain information concerning the exercise
of stock options during 1998 by each of the VERITAS named officers, including
the aggregate amount of gains on the date of exercise. In addition, the table
includes the number of shares covered by both vested and unvested stock options
held on December 31, 1998 by each of the VERITAS named officers. Also reported
are values for "in the money" stock options that represent the positive spread
between the respective exercise prices of outstanding stock options and the fair
market value of the VERITAS common stock as of
 
                                        6
<PAGE>   7
 
December 31, 1998. The fair market value is determined by the closing price of
VERITAS' common stock on December 31, 1998, which was $59.94 per share.
 
<TABLE>
<CAPTION>
                                                  NUMBER OF SECURITIES
                                                       UNDERLYING
                         SHARES        VALUE          UNEXERCISED          VALUE OF UNEXERCISED
                       ACQUIRED ON    REALIZED     OPTIONS AT FISCAL      IN-THE-MONEY OPTIONS AT
        NAME           EXERCISE(#)      ($)             YEAR-END            FISCAL YEAR-END($)
        ----           -----------   ----------   --------------------   -------------------------
                                                    VESTED   UNVESTED         VESTED      UNVESTED
                                                  --------    -------    -----------   -----------
<S>                    <C>           <C>          <C>        <C>         <C>           <C>
Mark Leslie..........    29,999      $  940,623   378,751     337,499    $19,043,997   $12,459,417
Geoffrey W. Squire...    86,400      $1,948,165   106,895     159,355    $ 5,094,057   $ 6,791,675
Fred van den Bosch...         0      $        0   290,801     181,312    $15,290,591   $ 6,194,667
Paul A. Sallaberry...    44,999      $1,710,374    83,617     138,661    $ 3,634,233   $ 5,306,142
Kenneth E. Lonchar...    13,706      $  667,551    11,895      41,537    $   413,934   $ 1,330,341
</TABLE>
 
     Share data has been restated to give retroactive effect to a 3-for-2 stock
split in the form of a stock dividend effected in May 1998. The value realized
for option exercises is the aggregate fair market value of VERITAS common stock
on the date of exercise less the exercise price. The valuations shown above for
unexercised in-the-money options are based on the difference between the option
exercise price and the fair market value of the stock on December 31, 1998.
These values have not been, and may never be, realized.
 
ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT
 
     The following table sets forth information as of March 31, 1999, or as
otherwise specified, with respect to the beneficial ownership of VERITAS common
stock by:
 
     -  each stockholder known by VERITAS to be the beneficial owner of more
        than 5% of the outstanding shares of VERITAS common stock;
 
     -  each director of VERITAS;
 
     -  the Chief Executive Officer and each of the four most highly compensated
        executive officers of VERITAS named for 1998; and
 
     -  all executive officers and directors of VERITAS as a group.
 
     The table reflects beneficial ownership as of March 31, 1999. We have
determined beneficial ownership in accordance with the rules of the Securities
and Exchange Commission. To our knowledge, the persons named in the table have
sole voting and investment power with respect to all shares shown as
beneficially owned by them subject to community property laws where applicable
unless we indicate otherwise below. However, we have not included any other
person's options for the purpose of computing percentage ownership.
 
     On March 31, 1999, there were 48,092,431 shares of VERITAS common stock
outstanding.
 
     Pilgrim Baxter and Associates, an institutional investment manager that
holds shares on behalf of various client accounts, shares voting power and holds
dispositive power with respect to its shares.
 
                                        7
<PAGE>   8
 
<TABLE>
<CAPTION>
                                             AMOUNT AND NATURE OF
                                             BENEFICIAL OWNERSHIP
                                       ---------------------------------    PERCENT OF
          BENEFICIAL OWNER              SHARES      OPTIONS      TOTAL        CLASS
          ----------------             ---------   ---------   ---------    ----------
<S>                                    <C>         <C>         <C>          <C>
William H. Janeway...................  6,675,650          --   6,675,650      13.88%
E.M. Warburg, Pincus & Co., LLC......  6,674,150          --   6,674,150      13.88
Warburg, Pincus & Company............  6,664,531          --   6,664,531      13.86
Warburg, Pincus Investors, L.P.......  6,660,650          --   6,660,650      13.85
Janus Capital Corporation............  5,347,915          --   5,347,915      11.12
  100 Fillmore Street, Suite 300
  Denver, CO 80206
Pilgrim Baxter and Associates........  2,703,288          --   2,703,288       5.62
  1255 Drummers Lane, Suite 300
  Wayne, PA 19087
Mark Leslie..........................    671,958     439,687   1,111,645       2.29
Geoffrey W. Squire...................    380,000     143,629     523,629       1.09
Fred van den Bosch...................     83,174     322,012     405,186          *
Paul A. Sallaberry...................     29,026     109,382     138,358          *
Joseph D. Rizzi......................     55,083      64,968     120,051          *
Kenneth E. Lonchar...................     51,522      16,583      68,105          *
Roel Pieper..........................         --      64,121      64,121          *
Steven Brooks........................      4,500      43,877      48,377          *
All current VERITAS executive
  officers and directors as a group
  (12 persons).......................  8,034,025   1,346,510   9,380,535      18.97%
</TABLE>
 
ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS
 
     From January 1, 1998 to the present, there have not been any and there are
currently no proposed transactions in which the amount involved exceeded $60,000
to which VERITAS or any of its subsidiaries was or is to be a party and in which
any executive officer, director, 5% beneficial owner of VERITAS common stock or
member of the immediate family of them had or will have a direct or indirect
material interest. There are no business relationships between VERITAS and any
entity, of which a director of VERITAS is an executive officer or of which a
director of VERITAS owns equity interest in excess of 10%, involving payments
for property or services in excess of five percent of VERITAS consolidated gross
revenues for VERITAS for 1998 except as previously reported or as set forth in
Item 11 above.
 
                                        8
<PAGE>   9
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized, in the City of Mountain View, State of
California, on the 29th day of April, 1999.
 
                                              VERITAS Software Corporation
                                              Registrant
 
                                                  /s/ KENNETH E. LONCHAR
                                              ----------------------------------
                                                      Kenneth E. Lonchar
                                                Senior Vice President, Finance
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below by the following persons on behalf of the
Registrant and in the capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                TITLE               DATE
                      ---------                                -----               ----
<C>                                                    <S>                    <C>
      PRINCIPAL EXECUTIVE OFFICER AND DIRECTOR:
 
                   /s/ MARK LESLIE                     President, Chief       April 29, 1999
-----------------------------------------------------  Executive Officer and
                     Mark Leslie                       Co-Chairman of the
                                                       Board
 
PRINCIPAL FINANCIAL OFFICER AND PRINCIPAL ACCOUNTING
OFFICER:
 
               /s/ KENNETH E. LONCHAR                  Senior Vice            April 29, 1999
-----------------------------------------------------  President, Finance
                 Kenneth E. Lonchar                    and Chief Financial
                                                       Officer
 
ADDITIONAL DIRECTORS:
 
               /s/ GEOFFREY W. SQUIRE                  Co-Chairman of the     April 29, 1999
-----------------------------------------------------  Board
                 Geoffrey W. Squire
 
               /s/ FRED VAN DEN BOSCH                  Director               April 29, 1999
-----------------------------------------------------
                 Fred van den Bosch
 
                  /s/ STEVEN BROOKS                    Director               April 29, 1999
-----------------------------------------------------
                    Steven Brooks
 
                 /s/ WILLIAM JANEWAY                   Director               April 29, 1999
-----------------------------------------------------
                   William Janeway
 
                                                       Director               April   , 1999
-----------------------------------------------------
                     Roel Pieper
 
                  /s/ JOSEPH RIZZI                     Director               April 29, 1999
-----------------------------------------------------
                    Joseph Rizzi
</TABLE>
 
                                        9