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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-04-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001212004</rptOwnerCik>
            <rptOwnerName>CRANDALL STEVEN J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ASHAWAY LINE &amp; TWINE MFG. CO. INC.</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 549</rptOwnerStreet2>
            <rptOwnerCity>ASHAWAY</rptOwnerCity>
            <rptOwnerState>RI</rptOwnerState>
            <rptOwnerZipCode>02804</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>2019-04-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>590</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2550</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1175</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Steven J Crandall TTEE Pamela Crandall TR-1990 U/A 1/11/90 FBO Steven J Crandall</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14848.263</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Steven J. Crandall Living Trust Dated 2/20/1990</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Balance reflects 800 shares which were previously owned directly by Steven J. Crandall and are now owned by the Steven J. Crandall Living Trust.</footnote>
        <footnote id="F2">Balance reflects acquisitions pursuant to dividend reinvestments exempt from Form 4 reporting under Rule 16a-11.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kristen L. DiSanto, Attorney-in-Fact</signatureName>
        <signatureDate>2019-04-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_155622315787609.xml", "description": "FORM 4", "secsgml_size_bytes": 5004}]
X0306
4
2019-04-23
0
0000737468
WASHINGTON TRUST BANCORP INC
WASH
0001212004
CRANDALL STEVEN J
ASHAWAY LINE & TWINE MFG. CO. INC.
P.O. BOX 549
ASHAWAY
RI
02804
1
0
0
0
Common Stock
2019-04-23
4
A
0
590
0
A
2550
D
Common Stock
1175
I
Steven J Crandall TTEE Pamela Crandall TR-1990 U/A 1/11/90 FBO Steven J Crandall
Common Stock
14848.263
I
Steven J. Crandall Living Trust Dated 2/20/1990
Balance reflects 800 shares which were previously owned directly by Steven J. Crandall and are now owned by the Steven J. Crandall Living Trust.
Balance reflects acquisitions pursuant to dividend reinvestments exempt from Form 4 reporting under Rule 16a-11.
/s/ Kristen L. DiSanto, Attorney-in-Fact
2019-04-25