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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-10-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001391437</issuerCik>
        <issuerName>Gabelli Healthcare &amp; WellnessRx Trust</issuerName>
        <issuerTradingSymbol>GRX.C</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001185533</rptOwnerCik>
            <rptOwnerName>GABELLI MARIO J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GAMCO INVESTORS, INC</rptOwnerStreet1>
            <rptOwnerStreet2>ONE CORPORATE CENTER</rptOwnerStreet2>
            <rptOwnerCity>RYE</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10580</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Control Person of Adviser</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Series C Cumulative Preferred Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2022-10-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>50000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>20</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>E3M 2018, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Series C Cumulative Preferred Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2022-10-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>50000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>20</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>175000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Series C Cumulative Preferred Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Associated Capital Group, Inc.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Series C Cumulative Preferred Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>190000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>MJG IV Limited Partnership</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Series C Cumulative Preferred Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>GPJ Retirement Partners</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares traded in a private transaction between related accounts</footnote>
        <footnote id="F2">The shares being reported are held at E3M 2018, LLC, in which Mr. Gabelli has less than a 100% interest and disclaims beneficial ownership of the shares held by it which are in excess of his indirect pecuniary interest.</footnote>
        <footnote id="F3">The shares reported reflect the total shares owned by Associated Capital Group, Inc. (AC).  Mario J. Gabelli is the Executive Chair and controlling shareholder of AC.  Mr. Gabelli has less than a 100% interest in AC and disclaims beneficial ownership of the shares held by it which are in excess of his indirect pecuniary interest.</footnote>
        <footnote id="F4">The shares reported reflect the total shares owned by MJG IV Limited Partnership, a limited partnership for which Mr. Gabelli serves as a general partner.  Mr. Gabelli has less than a 100% interest in the entity and disclaims beneficial ownership of the shares held by this entity which are in excess of his indirect pecuniary interest.</footnote>
        <footnote id="F5">The shares reported reflect the total shares owned by GPJ Retirement Partners, LLC, a limited liability company.  Mr. Gabelli has less than a 100% interest in the entity and disclaims beneficial ownership of the shares held by this entity which are in excess of his indirect pecuniary interest.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Douglas R. Jamieson as Attorney-in-Fact for Mario J. Gabelli</signatureName>
        <signatureDate>2022-10-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
