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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-03-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001040570</issuerCik>
        <issuerName>GeoEye, Inc.</issuerName>
        <issuerTradingSymbol>GEOY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000947822</rptOwnerCik>
            <rptOwnerName>FEINBERG STEPHEN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CERBERUS CAPITAL MANAGEMENT, L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>299 PARK AVENUE - 22ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10171</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2012-03-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>25000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.8561</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4771379</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By limited partnership and limited liability company</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">As of March 6, 2012, Cerberus Partners II, L.P. and Cerberus Series Four Holdings, LLC held 53,844 and 4,717,535 shares of common stock, par value $0.01 per share (the &quot;Common Stock&quot;), of GeoEye, Inc. (the &quot;Company&quot;), respectively.</footnote>
        <footnote id="F2">Stephen Feinberg, through one or more entities, possesses the sole power to vote and the sole power to direct the disposition of all securities of the Company held by Cerberus Partners II, L.P. and Cerberus Series Four Holdings, LLC.  Mr. Feinberg's interest in the securities reported herein is limited to the extent of his pecuniary interest in Cerberus Partners II, L.P. and Cerberus Series Four Holdings, LLC, if any.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Stephen Feinberg</signatureName>
        <signatureDate>2012-03-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
