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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2016-12-14</periodOfReport>

    <dateOfOriginalSubmission>2016-12-16</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000103145</issuerCik>
        <issuerName>VEECO INSTRUMENTS INC</issuerName>
        <issuerTradingSymbol>VECO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001497582</rptOwnerCik>
            <rptOwnerName>Miller William John</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VEECO INSTRUMENTS INC.</rptOwnerStreet1>
            <rptOwnerStreet2>TERMINAL DRIVE</rptOwnerStreet2>
            <rptOwnerCity>PLAINVIEW</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11803</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3362</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>78273</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were acquired pursuant to a restricted stock award under the Veeco Instruments Inc. 2010 Stock Incentive Plan and are subject to certain restrictions. These restrictions will lapse with respect to 1/4 of such shares on each of the first, second, third and fourth anniversaries of the date of grant, subject to the reporting person's continued service through such date. These shares were erroneously reported as restricted stock units on Table II on 12/16/2016.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Gregory A. Robbins, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
