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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-07-15</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001636422</issuerCik>
        <issuerName>Health Catalyst, Inc.</issuerName>
        <issuerTradingSymbol>HCAT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001089744</rptOwnerCik>
            <rptOwnerName>HAQUE PROMOD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>525 UNIVERSITY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 800</rptOwnerStreet2>
            <rptOwnerCity>PALO ALTO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94301</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-07-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>599361</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1753386</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Limited Partnership</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-07-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>600000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1752090</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Limited Partnership</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3557</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares were disposed of via a pro rata in-kind distribution of Issuer's stock from Norwest Venture Partners XI, LP (&quot;NVP XI&quot;) to its limited partners.</footnote>
        <footnote id="F2">The NVP XI distribution resulted in a change in the form of beneficial ownership so that following the distribution (i) 677 shares were beneficially owned by Haque Revocable Trust UA DTD 05/07/2002, of which Promod Haque is a Trustee, and (ii) 618 shares were beneficially owned by Haque Family Partners II, of which Promod Haque is a partner. The remaining 1,752,091 shares are held of record by NVP XI. By virtue of his position as a Co-Chief Executive Officer of NVP Associates, LLC (&quot;NVP Associates&quot;), the managing member of the general partner of NVP XI, Mr. Haque may be deemed to share voting and dispositive power with respect to such securities. Mr. Haque disclaims beneficial ownership of all such securities, except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F3">Shares were disposed of via a pro rata in-kind distribution of Issuer's stock from Norwest Venture Partners XII, LP (&quot;NVP XII&quot;) to its limited partners.</footnote>
        <footnote id="F4">The securities shown on Line 2 of Table I represent securities held of record by NVP XII. By virtue of his position as a Co-Chief Executive Officer of NVP Associates, the managing member of the general partner of NVP XII, Mr. Haque may be deemed to share voting and dispositive power with respect to such securities. Mr. Haque disclaims beneficial ownership of all such securities, except to the extent of any pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matthew De Dominicis, Attorney-in-fact</signatureName>
        <signatureDate>2020-07-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
