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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001704596</issuerCik>
        <issuerName>EVO Payments, Inc.</issuerName>
        <issuerTradingSymbol>EVOP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001182031</rptOwnerCik>
            <rptOwnerName>FINNEGAN PAUL J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 WEST MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001219630</rptOwnerCik>
            <rptOwnerName>MENCOFF SAMUEL M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MADISON DEARBORN PARTNERS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>70 WEST MADISON STREET, SUITE 4600</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Series A Convertible Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.80</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-04-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>152250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>985.2217</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock, $0.0001 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9636069</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>152250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of Series A Convertible Preferred Stock, par value $0.0001 per share (the &quot;Series A Preferred Stock&quot;) of EVO Payments, Inc. (the &quot;Issuer&quot;) is convertible into shares of the Issuer's Class A common stock, par value $0.0001 per share (the &quot;Class A Common Stock&quot;) at an initial conversion rate of 63.2911 shares of Common Stock for each share of Series A Preferred Stock, which represents an initial conversion price of approximately $15.80 per share of Class A Common Stock.  Holders of shares of Series A Preferred Stock are entitled to cumulative, paid-in-kind (&quot;PIK&quot;) dividends, which are payable semi-annually in arrears by increasing the liquidation preference for each outstanding share of Series A Preferred Stock.</footnote>
        <footnote id="F2">(Continued from Footnote 1) The number of shares of Class A Common Stock into which a share of Series A Preferred Stock will convert at any time is equal to the product of (i) the then-effective conversion rate, which is subject to customary anti-dilution and other adjustments, and (ii) the quotient obtained by dividing (a) the sum of the then-effective liquidation preference per share of Series A Preferred Stock and the amount of any accrued but unpaid PIK dividends by (b) the initial liquidation preference of $1,000.</footnote>
        <footnote id="F3">Reflects the purchase of Series A Preferred Stock pursuant to an Investment Agreement among the Issuer and certain affiliates of the reporting persons.</footnote>
        <footnote id="F4">The Series A Preferred Stock is convertible at any time, at the holder's election, after the earlier of (i) the date on which the Issuer obtains the Stockholder Approval (as defined hereafter, and which is expected to be sought at the Issuer's 2020 annual meeting of stockholders) and (ii) the date on which the holders of a majority of the Series A Preferred Stock then outstanding provide notice to the Issuer that it need no longer seek the Stockholder Approval (such notice shall not be delivered, if at all, prior to the earlier of (a) the date of the Issuer's 2021 annual meeting of stockholders and (b) August 1, 2021).</footnote>
        <footnote id="F5">(Continued from Footnote 4) Unless and until approval of the Issuer's stockholders is obtained as contemplated by Nasdaq listing rules (the &quot;Stockholder Approval&quot;), no holder of Series A Preferred Stock may convert shares of Series A Preferred Stock through either an optional or a mandatory conversion into shares of Class A Common Stock if and to the extent that such conversion would result in the holder beneficially owning in excess of 19.99% of the aggregate number of votes entitled to be cast generally at a meeting of the Company's stockholders held for the election of directors by all outstanding shares of the Company's common stock. Subject to certain conditions set forth in the Certificate of Designations, the Issuer may, at its election, require conversion of all of the outstanding shares of Series A Preferred Stock.</footnote>
        <footnote id="F6">The Series A Preferred Stock has no expiration date.</footnote>
        <footnote id="F7">These securities are held of record by MDCP Cardservices II, LLC (&quot;MDCP Cardservices II&quot;), a member-managed limited liability company.  Madison Dearborn Capital Partners VI-A, L.P. (&quot;MDCP VI-A&quot;) may be deemed to share beneficial ownership of the securities held by MDCP Cardservices II as its managing member. Madison Dearborn Partners VI-A&amp;C, L.P. (&quot;MDP VI-A&amp;C&quot;), as the general partner of MDCP VI-A, may be deemed to share beneficial ownership of the reported securities. Madison Dearborn Partners, LLC (&quot;MDP LLC&quot;), as the general partner of MDP VI-A&amp;C, may be deemed to share beneficial ownership of the reported securities. As the sole members of the limited partner committee of MDP VI-A&amp;C, which has the power, acting by unanimous vote, to vote or dispose of the securities beneficially owned by MDP VI-A&amp;C, Paul J. Finnegan and Samuel M. Mencoff may be deemed to have shared voting and investment power over such securities.</footnote>
        <footnote id="F8">Each of the reporting persons disclaims beneficial ownership of the reported securities except to the extent of his or its pecuniary interest therein. MDCP Cardservices II and MDCP VI-A have separately filed a Form 3.</footnote>
    </footnotes>

    <remarks>This Form 4 is filed by more than one reporting person and is a joint filing with the Form 4 filed by Madison Dearborn Partners, LLC and Madison Dearborn Partners VI-A&amp;C, L.P. on April 23, 2020 and the Form 3 filed by MDCP Cardservices II, LLC and MDCP VI-A and relates to the same transaction. Each of the reporting persons may be deemed a director by deputization as a result of Messrs. Vahe A. Dombalagian and Matthew W. Raino, Managing Directors of MDP LLC, serving on the board of directors of the Issuer, and as a result of the reporting persons having the right to nominate directors to the board of the Issuer pursuant to a Director Nomination Agreement.</remarks>

    <ownerSignature>
        <signatureName>/s/ Annie S. Terry, as Attorney-in-Fact</signatureName>
        <signatureDate>2020-04-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
