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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-06-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001447669</issuerCik>
        <issuerName>TWILIO INC</issuerName>
        <issuerTradingSymbol>TWLO</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001284038</rptOwnerCik>
            <rptOwnerName>ROTTENBERG ERIKA</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>101 SPEAR STREET, FIFTH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-06-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>199.0075</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30995</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported were executed under the Reporting Person's 10b5-1 trading plan, dated as of 12/10/2025.</footnote>
        <footnote id="F2">The reported price in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $199.00 to $199.075 per share, inclusive. The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or to the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F3">Shares are held by The Erika Rottenberg Revocable Trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Juliana Chen as attorney-in-fact for Reporting Person</signatureName>
        <signatureDate>2026-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
