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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001701108</issuerCik>
        <issuerName>Spero Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>SPRO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001720974</rptOwnerCik>
            <rptOwnerName>Mahadevia Ankit</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SPERO THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>675 MASSACHUSETTS AVENUE, 14TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02139</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CEO and President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12286</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.81</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>797832</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported transaction is a sale of common stock effected to cover tax withholding obligations in connection with the vesting of restricted stock units (&quot;RSUs&quot;) that were granted to the Reporting Person on February 1, 2022 pursuant to a &quot;sell to cover&quot; provision included in the RSU Agreement.</footnote>
        <footnote id="F2">Amount includes 65,817 shares of common stock held by the Mahadevia-Mehta Family Trust, of which the Reporting Person is a trustee. Amount also includes 691,205 RSUs held by the Reporting Person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Tamara Joseph, Attorney-in-Fact for Ankit Mahadevia</signatureName>
        <signatureDate>2023-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
