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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001391437</issuerCik>
        <issuerName>Gabelli Healthcare &amp; WellnessRx Trust</issuerName>
        <issuerTradingSymbol>GRX</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>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Control Person of Adviser</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, Par Value $0.001</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.0789</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>186037.66</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares, Par Value $0.001</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>282854</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>GGCP, Inc.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares, Par Value $0.001</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10122</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>MJG IV Limited Partnership</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares, Par Value $0.001</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5837</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>GPJ Retirement Partners</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Total includes shares acquired through dividend reinvestment subsequent to the initial purchase.</footnote>
        <footnote id="F2">The shares reported reflect the total shares owned by GGCP, Inc. (GGCP).  Mario J. Gabelli is the Chief Executive Officer, a director, and the controlling shareholder of GGCP.   Mr. Gabelli has less than a 100% interest in GGCP 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 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="F4">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>2020-03-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
