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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-11-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001492426</issuerCik>
        <issuerName>Horizon Pharma plc</issuerName>
        <issuerTradingSymbol>HZNP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001342821</rptOwnerCik>
            <rptOwnerName>Himawan Jeff</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HORIZON PHARMA PLC</rptOwnerStreet1>
            <rptOwnerStreet2>ADELAIDE CHAMBERS, PETER STREET</rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>8</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3450000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.05</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1614731</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Due to a clerical error, the number of ordinary shares reported in the Reporting Person's previous Form 4 filed September 22, 2014 was inadvertently overstated by 96 shares.  The number of ordinary shares indirectly owned by the Reporting Person prior to this transaction was 5,064,731.</footnote>
        <footnote id="F2">The securities are held directly by Essex Woodlands Health Ventures Fund VII, L.P. (the &quot;Fund&quot;). The Reporting Person is a manager of Essex Woodlands Health Ventures VII, L.L.C., which is the general partner of Essex Woodlands Health Ventures VII, L.P., the general partner of the Fund. The Reporting Person disclaims beneficial ownership of these securities, except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Paul W. Hoelscher, Attorney-in-Fact</signatureName>
        <signatureDate>2014-11-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
