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<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000029669</issuerCik>
        <issuerName>RR Donnelley &amp; Sons Co</issuerName>
        <issuerTradingSymbol>RRD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001685733</rptOwnerCik>
            <rptOwnerName>Pecaric John P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O R.R. DONNELLEY &amp; SONS COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>35 W. WACKER DRIVE</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60601</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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        <nonDerivativeTransaction>
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            <transactionDate>
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            <transactionTimeliness>
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                </transactionPricePerShare>
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    <derivativeTable>
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            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
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            <transactionDate>
                <value>2020-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7483</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7483</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>115284</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-12-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>62002</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>62002</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>75599</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
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    <footnotes>
        <footnote id="F1">Each share of phantom stock is payable in shares of common stock or cash.  The vested phantom stock was settled for cash.</footnote>
        <footnote id="F2">Shares acquired upon settlement of phantom Performance Stock Units granted on March 4, 2019.</footnote>
        <footnote id="F3">Shares acquired upon settlement of Performance Stock Units granted on March 4, 2019 and March 2, 2020.</footnote>
        <footnote id="F4">Phantom stock is payable in shares of common stock or cash in three equal installments, subject to reporting person's continued employment.</footnote>
    </footnotes>

    <remarks>On December 14, 2021, the Issuer entered into an Agreement and Plan of Merger, by and among the Issuer, Chatham Delta Parent, Inc. and Chatham Delta Acquisition Sub, Inc., providing for the merger of Chatham Delta Acquisition Sub, Inc. with and into the Issuer (the &quot;Merger&quot;), with the Issuer surviving as a wholly owned subsidiary of Chatham Delta Parent, Inc.  In connection with the Merger, to mitigate the potential impact of Section 280G and Section 4999 of the Internal Revenue Code of 1986, as amended, on the Issuer and the Reporting Person, the Board of Directors of the Issuer approved the acceleration of vesting of certain equity awards and equity-based awards, as described in this Form 4.</remarks>

    <ownerSignature>
        <signatureName>Deborah L. Steiner, Attorney-in-Fact for John P. Pecaric</signatureName>
        <signatureDate>2021-12-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
