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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000071691</issuerCik>
        <issuerName>NEW YORK TIMES CO</issuerName>
        <issuerTradingSymbol>NYT.A</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001546873</rptOwnerCik>
            <rptOwnerName>Green Steven B.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>THE NEW YORK TIMES COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>620 8TH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10018</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>Class A Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2016-01-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>17</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15615</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares acquired on January 28, 2016, in the form of Restricted Stock Units (&quot;RSUs&quot;) pursuant to a term of The New York Times Company 2010 Incentive Compensation Plan whereby additional RSUs are credited to an RSU holder's account in connection with, and with a value equal to, cash dividends paid on The New York Times Company's Class A Common Stock.  Vested shares will be delivered within 90 days following the cessation of the reporting person's membership on the Board of Directors.</footnote>
        <footnote id="F2">In addition, the reporting person may be deemed to have a pecuniary interest in 300,000 shares of Class A stock held indirectly, by his wife, as to which shares he disclaims beneficial ownership, 1,400,000 shares of Class A stock held indirectly, by a trust, 50,000 shares of Class A stock and 1,968 shares of Class A stock held indirectly, by two trusts, as to which shares he disclaims beneficial ownership.</footnote>
        <footnote id="F3">The reporting person disclaims beneficial ownership of the 10,000 shares of Class A stock held by Ordinance Capital LP, except to the extent of reporting person's pecuniary interest (approximately 75%) in the securities.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Theodore R. Wagner as Attorney-in-fact for Stephen B. Green</signatureName>
        <signatureDate>2016-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
