<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-11-13</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000939767</issuerCik>
        <issuerName>EXELIXIS INC</issuerName>
        <issuerTradingSymbol>EXEL</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001030575</rptOwnerCik>
            <rptOwnerName>FORMELA JEAN FRANCOIS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>890 WINTER STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WALTHAM</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02451</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector>
<isOfficer>0</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle></officerTitle>
<otherText></otherText>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeTable>
<nonDerivativeTransaction>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-11-13</value>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>S</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>10002</value>
</transactionShares>
<transactionPricePerShare>
<value>7.0998</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>D</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>1183185</value>
<footnoteId id="F1"/>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
<footnoteId id="F1"/>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>Partner AVA</value>
<footnoteId id="F1"/>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeTransaction>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-11-13</value>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>S</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>4998</value>
</transactionShares>
<transactionPricePerShare>
<value>7.0998</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>D</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>534683</value>
<footnoteId id="F2"/>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
<footnoteId id="F2"/>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>Partner AVA</value>
<footnoteId id="F2"/>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
</nonDerivativeTable>
<footnotes>
<footnote id="F1">Shares held by Atlas Venture Fund II LP (AVF) a part of Atlas Venture group of funds. Dr. Formela is a general partner of Atlas Venture Associates II LP (AVA). </footnote>
<footnote id="F2">Shares held by Atlas Europe Fund BV (AVEF) a part of Atlas Venture group of funds. Dr. Formela is a general partner of Atlas Venture Associates II LP (AVA)which is the general partner of AVF. Additional 54051 held by Atlas Venture Germany BV (AVG) and 16500 shares directly held by Dr. Formela.</footnote>
</footnotes>
<remarks></remarks>
<ownerSignature>
<signatureName>George Scangos/Attorney in Fact</signatureName>
<signatureDate>2003-11-14</signatureDate>
</ownerSignature>
</ownershipDocument>

