<?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>0001534522</rptOwnerCik>
            <rptOwnerName>Norwest Venture Partners XI, LP</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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001614660</rptOwnerCik>
            <rptOwnerName>Norwest Venture Partners XII, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>525 UNIVERSITY AVENUE, SUITE 800</rptOwnerStreet1>
            <rptOwnerStreet2></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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001535261</rptOwnerCik>
            <rptOwnerName>Crowe Jeffrey</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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001726084</rptOwnerCik>
            <rptOwnerName>Kossow Jon Erik</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>599939</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1752214</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </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>
    </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 123 shares were beneficially owned by Kossow Family Trust, of which Mr. Kossow is a Trustee. The remaining 1,752,091 shares are held of record by NVP XI. Genesis VC Partners XI, LLC (&quot;Genesis XI&quot;) is the general partner of NVP XI and may be deemed to have sole voting and dispositive power over the shares held by NVP XI. NVP Associates, LLC (&quot;NVP Associates&quot;), the managing member of Genesis XI, and Jeffrey Crowe and Jon E. Kossow, as Co-Chief Executive Officers of NVP Associates, may be deemed to share voting and dispositive power with respect to such securities. Such entities, Crowe and Kossow disclaim 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. Genesis VC Partners XII, LLC (&quot;Genesis XII&quot;) is the general partner of NVP XII and may be deemed to have sole voting and dispositive power over the shares held by NVP XII. NVP Associates, the managing member of Genesis XII, and Jeffrey Crowe and Jon E. Kossow, as Co-Chief Executive Officers of NVP Associates, may be deemed to share voting and dispositive power with respect to such securities. Such entities, Crowe and Kossow disclaim 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, Chief Financial Officer</signatureName>
        <signatureDate>2020-07-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
