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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-08-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001564406</issuerCik>
        <issuerName>Oak Street Health, Inc.</issuerName>
        <issuerTradingSymbol>?OSH?</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001793313</rptOwnerCik>
            <rptOwnerName>PRICE GEOFFREY M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O OAK STREET HEALTH, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>30 W. MONROE STREET, SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60603</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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                <value>Common stock, $0.001 par value</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
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            <transactionTimeliness>
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            </transactionTimeliness>
            <transactionAmounts>
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                    <value>7979989</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
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            <transactionTimeliness>
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        <derivativeTransaction>
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            <transactionTimeliness>
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            <transactionAmounts>
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                <transactionPricePerShare>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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    <footnotes>
        <footnote id="F1">These shares of common stock of Oak Street Health, Inc. (the &quot;Issuer&quot;) were issued in connection with the closing of the Issuer's initial public offering on August 10, 2020 (the &quot;Closing Date&quot;) in exchange for founders units and incentive units pursuant to the transactions contemplated by the Master Structuring Agreement dated August 10, 2020, by and among the Issuer, OSH Merger Sub 1, LLC, Quantum Strategic Partners Ltd., General Atlantic OSH Interholdco L.P., OSH Management Holdings, LLC (&quot;Management Holdings&quot;), Oak Street Health, LLC and Geoffrey Price dated August 10, 2020 (the &quot;Organizational Transactions&quot;).</footnote>
        <footnote id="F2">Represents shares of the Issuer's common stock, par value $0.001 (the &quot;Shares&quot;) issued in exchange for vested and unvested incentive units and founders units of Management Holdings in connection with the Organizational Transactions. The issuance of these securities was approved by the Issuer's board of directors under Rule 16b-3. Shares issued in exchange for the unvested incentive units were issued under the Oak Street Health Omnibus Incentive Plan (the &quot;Plan&quot;).</footnote>
        <footnote id="F3">Represents options issued under the Plan in exchange for vested incentive units in Management Holding in connection with the Organizational Transactions. Such options are fully vested and exercisable.</footnote>
        <footnote id="F4">Represents options issued under the Plan in exchange for unvested performance-vesting incentive units in Management Holdings in connection with the Organizational Transactions. These options will cliff vest 100% on August 10, 2022.</footnote>
        <footnote id="F5">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holdings in connection with the Organizational Transactions. These options will vest in three equal quarterly installments beginning on October 3, 2020.</footnote>
        <footnote id="F6">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions. These options will vest in five equal quarterly installments beginning on August 18, 2020.</footnote>
        <footnote id="F7">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions. These options will vest in eight equal quarterly installments beginning on October 23, 2020.</footnote>
        <footnote id="F8">Represents options issued under the Plan in exchange for unvested performance-vesting incentive units in Management Holdings in connection with the Organizational Transactions. These options will cliff vest 100% on June 14, 2023.</footnote>
        <footnote id="F9">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions. These options will vest in twelve equal quarterly installments beginning on August 15, 2020.</footnote>
        <footnote id="F10">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions. These options will cliff vest 100% on January 1, 2021.</footnote>
        <footnote id="F11">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions.  These options will vest 50% on each of January 1, 2022 and January 1, 2023.</footnote>
        <footnote id="F12">Represents options issued under the Plan in exchange for unvested performance-vesting incentive units in Management Holdings in connection with the Organizational Transactions. These options will cliff vest 100% on August 10, 2023.</footnote>
        <footnote id="F13">Represents options issued under the Plan in exchange for unvested time-vesting incentive units in Management Holding in connection with the Organizational Transactions. These options will vest 25% beginning on June 11, 2021 and then in twelve equal quarterly installments beginning on September 11, 2021.</footnote>
    </footnotes>

    <remarks>Chief Operating Officer, Director</remarks>

    <ownerSignature>
        <signatureName>/s/ Robert Guenthner, as attorney-in-fact for Geoffrey Price</signatureName>
        <signatureDate>2020-08-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
