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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2014-09-19</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <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>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Paul W. Hoelscher, Attorney-in-Fact</signatureName>
        <signatureDate>2014-09-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
