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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-06-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001212005</rptOwnerCik>
            <rptOwnerName>DEVAULT DAVID V</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2 DENNIS COURT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WESTERLY</rptOwnerCity>
            <rptOwnerState>RI</rptOwnerState>
            <rptOwnerZipCode>02891</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Chair, Secretary and CFO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>38.33</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50471.6227</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-15</value>
            </transactionDate>
            <transactionCoding>
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                <transactionCode>S</transactionCode>
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            </transactionCoding>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                <transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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            </transactionDate>
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            </transactionCoding>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            </transactionCoding>
            <transactionAmounts>
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                    <value>100</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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                </directOrIndirectOwnership>
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        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46571.6227</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>298</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.46</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46273.6227</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>102</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.47</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46171.6227</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David V. Devault</signatureName>
        <signatureDate>2015-06-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2015-06-15
0
0000737468
WASHINGTON TRUST BANCORP INC
WASH
0001212005
DEVAULT DAVID V
2 DENNIS COURT
WESTERLY
RI
02891
0
1
0
0
Vice Chair, Secretary and CFO
Common Stock
2015-06-15
4
S
0
670
38.33
D
50471.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3356
D
50371.6227
D
Common Stock
2015-06-15
4
S
0
100
38.34
D
50271.6227
D
Common Stock
2015-06-15
4
S
0
100
38.342
D
50171.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3472
D
50071.6227
D
Common Stock
2015-06-15
4
S
0
200
38.35
D
49871.6227
D
Common Stock
2015-06-15
4
S
0
100
38.36
D
49771.6227
D
Common Stock
2015-06-15
4
S
0
100
38.37
D
49671.6227
D
Common Stock
2015-06-15
4
S
0
200
38.38
D
49471.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3851
D
49371.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3881
D
49271.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3893
D
49171.6227
D
Common Stock
2015-06-15
4
S
0
500
38.39
D
48671.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3901
D
48571.6227
D
Common Stock
2015-06-15
4
S
0
100
38.3917
D
48471.6227
D
Common Stock
2015-06-15
4
S
0
600
38.40
D
47871.6227
D
Common Stock
2015-06-15
4
S
0
200
38.41
D
47671.6227
D
Common Stock
2015-06-15
4
S
0
100
38.4108
D
47571.6227
D
Common Stock
2015-06-15
4
S
0
100
38.4125
D
47471.6227
D
Common Stock
2015-06-15
4
S
0
300
38.42
D
47171.6227
D
Common Stock
2015-06-15
4
S
0
100
38.43
D
47071.6227
D
Common Stock
2015-06-15
4
S
0
100
38.4383
D
46971.6227
D
Common Stock
2015-06-15
4
S
0
400
38.44
D
46571.6227
D
Common Stock
2015-06-15
4
S
0
298
38.46
D
46273.6227
D
Common Stock
2015-06-15
4
S
0
102
38.47
D
46171.6227
D
/s/ David V. Devault
2015-06-17