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<ownershipDocument>

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    <documentType>4</documentType>

    <periodOfReport>2023-08-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001806347</issuerCik>
        <issuerName>Westrock Coffee Co</issuerName>
        <issuerTradingSymbol>WEST</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000014661</rptOwnerCik>
            <rptOwnerName>BROWN BROTHERS HARRIMAN &amp; CO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001642711</rptOwnerCik>
            <rptOwnerName>BBH Capital Partners V, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001642712</rptOwnerCik>
            <rptOwnerName>BBH Capital Partners V-A, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001805212</rptOwnerCik>
            <rptOwnerName>BBH CPV WCC Co-Investment LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001952856</rptOwnerCik>
            <rptOwnerName>Meskin Jeffrey B.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001934635</rptOwnerCik>
            <rptOwnerName>Kruczek Robert Patrick</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001952865</rptOwnerCik>
            <rptOwnerName>Paquin Jean-Pierre</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001952858</rptOwnerCik>
            <rptOwnerName>Langer Bradley M.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001953300</rptOwnerCik>
            <rptOwnerName>Boylan Michael A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>140 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-08-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1061158</value>
                    <footnoteId id="F8"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1061158</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-08-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>21443</value>
                    <footnoteId id="F8"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21443</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-08-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>794087</value>
                    <footnoteId id="F8"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>794087</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects securities directly held by BBH Capital Partners V, L.P. (&quot;BBH CPV&quot;).</footnote>
        <footnote id="F2">Reflects securities directly held by BBH Capital Partners V-A, L.P. (&quot;BBH CPV-A&quot;).</footnote>
        <footnote id="F3">Reflects securities directly held by BBH CPV WCC Co-Investment LLC. (&quot;BBH CPV Co-Invest&quot;).</footnote>
        <footnote id="F4">BBH Capital Partners (&quot;BBHCP&quot;) manages private equity investments through its funds, including BBH CPV, BBH CPV-A and BBH CPV Co-Invest (the &quot;Record Holders&quot;).  Each of the Record Holders are controlled and managed by a general partner, BBH Private Capital Management V, LLC (the &quot;General Partner&quot;).  Brown Brothers Harriman &amp; Co. (&quot;BBH&quot;), a New York limited partnership, serves as the managing member of the General Partner.</footnote>
        <footnote id="F5">BBH has designated each of Jeffrey Meskin, Patrick Kruczek, JP Paquin, Bradley Langer and Michael Boylan, as the sole and exclusive persons at BBH having voting power (including the power to vote or to direct the vote) and investment power (including the power to dispose or to direct the disposition) with respect to all securities held by the Record Holders. Each Reporting Person disclaims beneficial ownership of the reported securities except to the extent of their pecuniary interest therein.</footnote>
        <footnote id="F6">Information with respect to each of the Reporting Persons is given solely by such Reporting Person, and no Reporting Person has responsibility for the accuracy or completeness of information supplied by another Reporting Person.</footnote>
        <footnote id="F7">Each of the Reporting Persons (other than to the extent it directly holds securities reported herein) disclaims beneficial ownership of the securities held by the other Reporting Persons, except to the extent of such Reporting Person's pecuniary interest therein, and, pursuant to Rule 16a-1(a)(4) under the Securities Exchange Act of 1934 (the &quot;Exchange Act&quot;), each of the Reporting Persons (other than to the extent it directly holds securities reported herein) states that the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all of the securities reported herein for purposes of Section 16 of the Exchange Act or for any other purpose.</footnote>
        <footnote id="F8">As disclosed in a Current Report on Form 8-K filed by the Issuer on August 9, 2023, each of the Record Holders entered into subscription agreements with the Issuer on July 24, 2023 pursuant to which the Record Holders exercised preemptive rights under the Investor Rights Agreement, dated April 4, 2022, by and among the Issuer, the Record Holders and certain other parties thereto, and the Issuer agreed to issue and sell 1,876,688 Common Shares in the aggregate to the Record Holders at a purchase price per share of $10 (the &quot;BBH Preemptive Rights Investment&quot;). On August 7, 2023, the Company consummated the BBH Preemptive Rights Investment.</footnote>
        <footnote id="F9">In addition to the holdings of Common Stock listed here, BBH indirectly holds (i) 10,919,673 shares of Series A Convertible Preferred Stock through BBH CPV, (ii) 220,654 shares of Series A Convertible Preferred Stock through BBH CPV-A and (iii) 8,171,430 shares of Series A Convertible Preferred Stock through BBH CPV Co-Invest.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>BROWN BROTHERS HARRIMAN &amp; CO., By: /s/ Jeffrey B. Meskin, Partner</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BBH CAPITAL PARTNERS V, L.P., By: BBH Private Capital Management V, LLC, its general partner, By: /s/ Jeffrey B. Meskin, Title: Partner of BBH &amp; Co., Managing Member of BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BBH CAPITAL PARTNERS V-A, L.P., By: BBH Private Capital Management V, LLC, its general partner, By: /s/ Jeffrey B. Meskin, Title: Partner of BBH &amp; Co., Managing Member of BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>BBH CPV WCC CO-INVESTMENT LLC, By: BBH Private Capital Management V, LLC, its manager, By: /s/ Jeffrey B. Meskin, Title: Partner of BBH &amp; Co., Managing Member of BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Jeffrey B. Meskin, Partner, Brown Brothers Harriman &amp; Co.; Managing Member, BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Patrick Kruczek, Principal, Brown Brothers Harriman &amp; Co.; Managing Member, BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ JP Paquin, Partner, Brown Brothers Harriman &amp; Co.; Managing Member, BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Bradley Langer, Principal, Brown Brothers Harriman &amp; Co.; Managing Member, BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Michael Boylan, Principal, Brown Brothers Harriman &amp; Co.; Managing Member, BBH Private Capital Management V, LLC</signatureName>
        <signatureDate>2023-09-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
