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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-04-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000737468</issuerCik>
        <issuerName>WASHINGTON TRUST BANCORP INC</issuerName>
        <issuerTradingSymbol>WASH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001548238</rptOwnerCik>
            <rptOwnerName>Santos Edwin J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>234 MOURNING DOVE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAUNDERSTOWN</rptOwnerCity>
            <rptOwnerState>RI</rptOwnerState>
            <rptOwnerZipCode>02874</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-04-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>50.4953</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5250</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reported price is a weighted average with a range in price from $50.44 to $50.53.  The breakdown of actual transactions will be available upon request.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kristen L. DiSanto, Attorney-in-Fact</signatureName>
        <signatureDate>2019-04-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-04-26
0
0000737468
WASHINGTON TRUST BANCORP INC
WASH
0001548238
Santos Edwin J
234 MOURNING DOVE DRIVE
SAUNDERSTOWN
RI
02874
1
0
0
0
Common Stock
2019-04-26
4
S
0
300
50.4953
D
5250
D
The reported price is a weighted average with a range in price from $50.44 to $50.53.  The breakdown of actual transactions will be available upon request.
/s/ Kristen L. DiSanto, Attorney-in-Fact
2019-04-29