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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-02-01</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001578845</issuerCik>
        <issuerName>Allergan plc</issuerName>
        <issuerTradingSymbol>AGN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001314021</rptOwnerCik>
            <rptOwnerName>Brown Adriane M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CLONSHAUGH BUSINESS AND TECHNOLOGY PARK,</rptOwnerStreet1>
            <rptOwnerStreet2>COOLOCK, CO.</rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>D17 E400</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <remarks>Exhibit List:  Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ A. Robert D. Bailey, Attorney-in-Fact for the Reporting Person</signatureName>
        <signatureDate>2017-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
