<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-05-23</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001439404</issuerCik>
        <issuerName>ZYNGA INC</issuerName>
        <issuerTradingSymbol>ZNGA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001337679</rptOwnerCik>
            <rptOwnerName>GIBEAU FRANK D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ZYNGA INC.</rptOwnerStreet1>
            <rptOwnerStreet2>699 8TH STREET</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94103</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-05-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1693310</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-05-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-03-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
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            </conversionOrExercisePrice>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
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            <expirationDate>
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            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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            <ownershipNature>
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                </directOrIndirectOwnership>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            </transactionAmounts>
            <exerciseDate>
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            <expirationDate>
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            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
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            </conversionOrExercisePrice>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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            </transactionAmounts>
            <exerciseDate>
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            <expirationDate>
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            </expirationDate>
            <underlyingSecurity>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            <conversionOrExercisePrice>
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            <transactionDate>
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            </transactionCoding>
            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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        </derivativeTransaction>
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                </transactionShares>
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            <transactionAmounts>
                <transactionShares>
                    <value>221483</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>221483</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reported amount reflects shares transferred from the Reporting Person.</footnote>
        <footnote id="F2">Pursuant to the Agreement and Plan of Merger, dated as of January 9, 2022 (the &quot;Merger Agreement&quot;), by and among Take-Two Interactive Software, Inc. (&quot;Take-Two&quot;), Zebra MS I, Inc., Zebra MS II, Inc., and the Issuer, each share of the Issuer's class A common stock was cancelled and converted into the right to receive (i) 0.0406 shares of Take-Two common stock and (ii) $3.50 in cash, together with cash in lieu of any fractional shares of Take-Two common stock.</footnote>
        <footnote id="F3">Shares held directly by Frank Donald Gibeau Trust U/A DTD 12/13/2019. Mr. Gibeau serves as trustee and holds voting and dispositive power with respect to these shares.</footnote>
        <footnote id="F4">Pursuant to the Merger Agreement, at the effective time, each outstanding option was assumed and converted into an option to purchase the number of shares of Take-Two common stock (rounded down to the nearest whole share) determined by multiplying (i) the number of shares of class A common stock subject to the Issuer option immediately prior to the Effective Time by (ii) 0.0702, with an exercise price determined by dividing (i) the exercise price of the Issuer option immediately prior to the Effective Time by (ii) 0.0702. The converted option will otherwise be subject to the same terms and conditions as were applicable to the Issuer option prior to the effective time.</footnote>
        <footnote id="F5">Each restricted stock unit represents a contingent right to receive 1 share of the Issuer's Class A Common Stock upon vest.</footnote>
        <footnote id="F6">Pursuant to the Merger Agreement, at the effective time, each of the Issuer's restricted stock units was assumed and converted into a restricted stock unit with respect to a number of shares of Take-Two common stock (rounded down to the nearest whole share) determined by multiplying (i) the number of shares of class A common stock subject to the Issuer restricted stock unit immediately prior to the Effective Time by (ii) 0.0702. The converted restricted stock unit will otherwise be subject to the same terms and conditions as were applicable to the Issuer restricted stock units prior to the effective time.</footnote>
        <footnote id="F7">Pursuant to the Merger Agreement, at the effective time, each of the Issuer's performance stock units was assumed and converted into a performance stock unit with respect to a number of shares of Take-Two common stock (rounded down to the nearest whole share) determined by multiplying (i) the number of shares of class A common stock subject to the Issuer performance stock unit immediately prior to the Effective Time by (ii) 0.0702. The converted performance stock unit will otherwise be subject to the same terms and conditions as were applicable to the Issuer performance stock units prior to the effective time.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matt Tolland, as attorney-in-fact for Frank D. Gibeau</signatureName>
        <signatureDate>2022-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
