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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-02-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001493594</issuerCik>
        <issuerName>MACOM Technology Solutions Holdings, Inc.</issuerName>
        <issuerTradingSymbol>MTSI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001239366</rptOwnerCik>
            <rptOwnerName>CHUNG PETER Y</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SUMMIT PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>222 BERKELEY STREET, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</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>2017-02-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1201635</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.55</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17416</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Remarks.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares sold by the following entities: 749,394 shares of common stock sold by Summit Partners Private Equity Fund VII-A, L.P.; 450,099 shares of common stock sold by Summit Partners Private Equity Fund VII-B, L.P.; 2,001 shares of common stock sold by Summit Investors I, LLC; 141 shares of common stock sold by Summit Investors I (UK), L.P.</footnote>
        <footnote id="F2">Represents shares and restricted stock units in the name of Peter Y. Chung, which are held for the benefit of Summit Partners, L.P.</footnote>
    </footnotes>

    <remarks>Summit Partners, L.P. is the managing member of Summit Partners PE VII, LLC, which is the general partner of Summit Partners PE VII, L.P., which is the general partner of each of Summit Partners Private Equity Fund VII-A, L.P. and Summit Partners Private Equity Fund VII-B, L.P. Summit Master Company, LLC is the managing member of Summit Investors Management, LLC, which is the manager of Summit Investors I, LLC, and the general partner of Summit Investors I (UK), L.P. Summit Master Company, LLC, as the managing member of Summit Investors Management, LLC has delegated investment decisions, including voting and dispositive power, to Summit Partners, L.P. and its Investment Committee responsible for voting and investment decisions with respect to the Issuer. Summit Partners, L.P., through a two-person Investment Committee responsible for voting and investment decisions with respect to the Issuer, currently composed of Martin J. Mannion and Peter Y. Chung, has voting and dispositive authority over the shares held by each of these entities and therefore may be deemed to beneficially own such shares. In addition, Mr. Chung is a member of Summit Master Company, LLC. Each of the Summit entities mentioned herein, Summit Partners, L.P., Summit Master Company, LLC, Mr. Mannion and Mr. Chung disclaims beneficial ownership of the shares of Common Stock and the restricted stock units, except to the extent of their pecuniary interest therein.</remarks>

    <ownerSignature>
        <signatureName>Robin W. Devereux, Power of Attorney for Peter Y. Chung</signatureName>
        <signatureDate>2017-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
