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

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-05-02</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001793308</rptOwnerCik>
            <rptOwnerName>PYKOSZ MICHAEL T</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>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, $0.001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6126706</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, $0.001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>790273</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Through Mike Pykosz Gift Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, $0.001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>250000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Through Lindsay Pykosz Revocable Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4946638</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-08-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, $0.001 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4946638</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>168052</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-08-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, $0.001 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>168052</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Through Mike Pykosz Gift Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.75</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1585677</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-02-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, $0.001 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1585677</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to that certain Agreement and Plan of Merger, dated as of February 7, 2023 (the &quot;Merger Agreement&quot;), by and among the Issuer, CVS Pharmacy, Inc. (&quot;Parent&quot;), Halo Merger Sub Corp. (&quot;Merger Sub&quot;) and, for the limited purposes set forth therein, CVS Health Corporation (&quot;CVS Health&quot;), Merger Sub merged with and into the Issuer (the &quot;Merger&quot;), with the Issuer surviving the Merger as a wholly-owned subsidiary of Parent. At the effective time of the Merger (the &quot;Effective Time&quot;), each share of the Issuer's common stock that was issued and outstanding immediately prior to the Effective Time was automatically cancelled and converted into the right to receive $39.00 per share in cash, without interest and subject to applicable tax withholdings (the &quot;Per Share Price&quot;).</footnote>
        <footnote id="F2">The shares of the Issuer's common stock reported as disposed by the Reporting Person include restricted stock awards which were, at the Effective Time, automatically assumed by Parent and converted into a corresponding CVS Health restricted stock award, as provided under the Merger Agreement.</footnote>
        <footnote id="F3">The shares of the Issuer's common stock reported as disposed by the Reporting Person include: (a) vested restricted stock units (&quot;RSUs&quot;) of the Issuer which, pursuant to the Merger Agreement, were, at the Effective Time, automatically canceled and converted into the right to receive an amount in cash (without interest and subject to applicable tax withholdings) equal to the Per Share Price multiplied by the number of shares of the Issuer's common stock subject to such RSUs as of immediately prior to the Effective Time, and (b) unvested RSUs of the Issuer granted on or after February 7, 2023 which were, at the Effective Time, automatically assumed by Parent and converted into a corresponding CVS Health RSU award, subject to the terms and conditions (including applicable vesting provisions) as provided under the Merger Agreement.</footnote>
        <footnote id="F4">The shares of the Issuer's common stock reported as disposed on this Form 4 reflects a correction to the Reporting Person's Form 4 filed on January 5, 2022, which inadvertently reported the acquisition by the Reporting Person of 417 shares of the Issuer's common stock pursuant to the Oak Street Health, Inc. 2020 Employee Stock Purchase Plan as a disposition rather than an acquisition of shares of the Issuer's common stock (resulting in the Reporting Person's direct beneficial ownership being understated by 834 shares), as well as a correction to the Reporting Person's Form 4 filed on March 22, 2023, which incorrectly reported 7,604,280 shares of the Issuer's common stock as beneficially owned directly by the Reporting Person following the reported transaction.</footnote>
        <footnote id="F5">Pursuant to the Merger Agreement, at the Effective Time, (a) the vested portion of this option was automatically cancelled and converted into the right to receive an amount in cash (without interest and subject to applicable tax withholdings) equal to the number of shares of the Issuer's common stock subject to such option as of immediately prior to the Effective Time multiplied by the excess of the Per Share Price over the exercise price per share of such vested portion of the option and</footnote>
        <footnote id="F6">(Continued from Footnote 5) (b) the unvested portion of this option was automatically cancelled and converted into the contractual right to receive a payment in cash (without interest and subject to applicable tax withholding) equal to the number of shares of the Issuer's common stock subject to such unvested portion of the option as of immediately prior to the Effective Time multiplied by the excess of the Per Share Price over the exercise price per share of such option, subject to the same terms and conditions (including applicable vesting provisions) as applied to such option immediately prior to the Effective Time, except as provided under the Merger Agreement.</footnote>
        <footnote id="F7">Pursuant to the Merger Agreement, at the Effective Time, this option was automatically cancelled and converted into the right to receive an amount in cash (without interest and subject to applicable tax withholdings) equal to the number of shares of the Issuer's common stock subject to such option as of immediately prior to the Effective Time multiplied by the excess of the Per Share Price over the exercise price per share of such option.</footnote>
        <footnote id="F8">The performance-based stock options (&quot;PSOs&quot;) were, at the Effective Time, automatically cancelled and converted into the contractual right to receive an amount in cash (without interest and subject to applicable tax withholdings) equal to the number of shares of the Issuer's common stock underlying such PSOs as of immediately prior to the Effective Time multiplied by the excess of the Per Share Price over the exercise price per share of such PSOs on December 31, 2023.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Robert Guenthner, attorney-in-fact for Michael T. Pykosz</signatureName>
        <signatureDate>2023-05-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
