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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001757898</issuerCik>
        <issuerName>STERIS plc</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001413087</rptOwnerCik>
            <rptOwnerName>Rosebrough Walter M Jr</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 70 SIR JOHN ROGERSON'S QUAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>2</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2019-06-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2179</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>134.07</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52123</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote Below.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">2,179 shares were withheld from the 4,681 restricted shares that vested on May 28, 2019. These 2,179 ordinary shares represent the value of the taxes required to be withheld pursuant to applicable employment or tax laws, as determined by the Issuer. These 4,681 ordinary shares were awarded to Mr. Rosebrough on June 1, 2016 as part of an award of 18,724 restricted shares. These vested shares were valued at the NYSE closing market price on June 3, 2019. The remaining restrictions on these ordinary shares lapse as follows: 4,681 on June 1, 2020.</footnote>
        <footnote id="F2">These 52,123 ordinary shares are held by the reporting person as trustee of a revocable trust established for his benefit. 32,360 of these ordinary shares are restricted. The restrictions on these ordinary shares lapse as follows: 4,681 on June 1, 2020; 4,000 on June 1, 2020; 3,097 on June 1, 2020; 2,597 on June 1, 2020; 4,000 on June 1, 2021; 3,097 on June 1, 2021; 2,597 on June 1, 2021; 3,097 on May 31, 2022; 2,597 on May 31, 2022; and 2,597 on May 31, 2023.</footnote>
        <footnote id="F3">These ordinary shares are held by the reporting person's spouse as trustee of a revocable trust established for her benefit.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ronald E. Snyder, Authorized Representative under Power of Attorney</signatureName>
        <signatureDate>2019-06-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
