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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-07-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001434316</issuerCik>
        <issuerName>FATE THERAPEUTICS INC</issuerName>
        <issuerTradingSymbol>FATE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001655472</rptOwnerCik>
            <rptOwnerName>TAHL CINDY</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FATE THERAPEUTICS, INC.;</rptOwnerStreet1>
            <rptOwnerStreet2>3535 GENERAL ATOMICS COURT #200</rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92121</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>General Counsel and Secretary</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-07-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>7.87</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            </transactionDate>
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            </transactionTimeliness>
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                </transactionShares>
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                </transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
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                <footnoteId id="F2"/>
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                </transactionShares>
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                </transactionAcquiredDisposedCode>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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        <nonDerivativeTransaction>
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            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                    <footnoteId id="F3"/>
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                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            </transactionDate>
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                <footnoteId id="F1"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1145</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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        <nonDerivativeTransaction>
            <securityTitle>
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    </nonDerivativeTable>

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                <transactionPricePerShare>
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            <expirationDate>
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                <transactionPricePerShare>
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            </securityTitle>
            <conversionOrExercisePrice>
                <value>6.55</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-07-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>15383</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F11"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15383</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>166643</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the Reporting Person on June 10, 2020.</footnote>
        <footnote id="F2">This transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the Reporting Person on January 8, 2021.</footnote>
        <footnote id="F3">Represents the weighted average sale price of the shares sold ranging from $86.47 to $86.65 per share. The Reporting Person will provide, upon request by the Commission staff, the Issuer, or a security holder of the Issuer, full information regarding the number of shares sold at each price within the ranges set forth in footnotes 3 through 10.</footnote>
        <footnote id="F4">Represents the weighted average sale price of the shares sold ranging from $87.50 to $88.28 per share.</footnote>
        <footnote id="F5">Represents the weighted average sale price of the shares sold ranging from $88.65 to $89.48 per share.</footnote>
        <footnote id="F6">Represents the weighted average sale price of the shares sold ranging from $89.78 to $90.68 per share.</footnote>
        <footnote id="F7">Represents the weighted average sale price of the shares sold ranging from $90.81 to $91.64 per share.</footnote>
        <footnote id="F8">Represents the weighted average sale price of the shares sold ranging from $91.88 to $92.41 per share.</footnote>
        <footnote id="F9">Represents the weighted average sale price of the shares sold ranging from $93.21 to $93.54 per share.</footnote>
        <footnote id="F10">Represents the weighted average sale price of the shares sold ranging from $94.22 to $95.12 per share.</footnote>
        <footnote id="F11">This option is fully vested.</footnote>
    </footnotes>

    <remarks>General Counsel and Secretary</remarks>

    <ownerSignature>
        <signatureName>/s/ Cindy Tahl</signatureName>
        <signatureDate>2021-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
