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

    <schemaVersion>X0306</schemaVersion>

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    <periodOfReport>2021-09-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001361983</issuerCik>
        <issuerName>ORBCOMM Inc.</issuerName>
        <issuerTradingSymbol>ORBC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001373568</rptOwnerCik>
            <rptOwnerName>Le Brun Christian</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ORBCOMM INC.</rptOwnerStreet1>
            <rptOwnerStreet2>395 W. PASSAIC STREET, SUITE 325</rptOwnerStreet2>
            <rptOwnerCity>ROCHELLE PARK</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07662</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP &amp; General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <expirationDate>
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        <derivativeTransaction>
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                <value>Stock Appreciation Right</value>
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            <transactionDate>
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                <transactionPricePerShare>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit (Time Vested)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
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            <transactionDate>
                <value>2021-09-01</value>
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            <transactionTimeliness>
                <value></value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                <directOrIndirectOwnership>
                    <value>D</value>
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            <securityTitle>
                <value>Performance Right (Performance Unit Award)</value>
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                <value></value>
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                <transactionShares>
                    <value>20739</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
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                    <value>D</value>
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                <footnoteId id="F5"/>
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                <footnoteId id="F5"/>
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                    <value>Common Stock</value>
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    </derivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;) by and among GI DI Orion Acquisition Inc., a Delaware corporation (&quot;Parent&quot;), GI DI Orion Merger Sub Inc., a Delaware corporation and wholly owned subsidiary of Parent, and ORBCOMM Inc., a Delaware corporation, in exchange for $11.50 per share upon the consummation of the transactions contemplated by the Merger Agreement (the &quot;Merger&quot;).  The Merger closed on September 1, 2021.</footnote>
        <footnote id="F2">Upon consummation of the Merger, each such stock appreciation right was canceled in exchange for a cash payment equal to the difference between $11.50 and the exercise price of the stock appreciation right.</footnote>
        <footnote id="F3">Upon consummation of the Merger, each time-based restricted stock unit was cancelled in exchange for a cash payment equal to $11.50.</footnote>
        <footnote id="F4">Upon consummation of the Merger, a number of performance-vesting restricted stock units equal to the &quot;target&quot; level was cancelled in exchange for a cash payment equal to $11.50 and any remaining performance-vesting restricted stock units were cancelled for no consideration.</footnote>
        <footnote id="F5">Upon consummation of the Merger, these performance unit awards were cancelled in exchange for a cash payment equal to $238,500.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christian Le Brun</signatureName>
        <signatureDate>2021-09-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
