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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-09-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001720821</issuerCik>
        <issuerName>Gores Holdings III, Inc.</issuerName>
        <issuerTradingSymbol>GRSH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001720903</rptOwnerCik>
            <rptOwnerName>Gores Sponsor III LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GORES HOLDINGS III, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>9800 WILSHIRE BLVD.</rptOwnerStreet2>
            <rptOwnerCity>BEVERLY HILLS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90212</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001694360</rptOwnerCik>
            <rptOwnerName>AEG Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GORES HOLDINGS III, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>9800 WILSHIRE BLVD.</rptOwnerStreet2>
            <rptOwnerCity>BEVERLY HILLS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90212</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001322454</rptOwnerCik>
            <rptOwnerName>Gores Alec E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GORES HOLDINGS III, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>9800 WILSHIRE BLVD.</rptOwnerStreet2>
            <rptOwnerCity>BEVERLY HILLS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90212</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class F Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-09-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>75000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.002</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>75000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10706250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Class F Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-10-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>781250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>781250</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9925000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the Amended and Restated Certificate of Incorporation of the Issuer, shares of Class F common stock, par value $0.0001 per share (the &quot;Class F Shares&quot;) have no expiration date and (i) are convertible into shares of Class A common stock, par value $0.0001 per share (&quot;Class A Shares&quot;), of the Issuer at any time at the option of the holder on a one-for-one basis and (ii) will automatically convert into Class A Shares at the time of the Issuer's initial business combination on a one-for-one basis, in each case, subject to adjustment.</footnote>
        <footnote id="F2">Prior to the Issuer's initial public offering, Gores Sponsor III LLC (the &quot;Sponsor&quot;) sold an aggregate of 75,000 shares to the Issuer's independent directors.</footnote>
        <footnote id="F3">The Class F Shares are held directly by the Sponsor. The managing member of the Sponsor is AEG Holdings, LLC (&quot;AEG&quot;). Alec Gores is the managing member of AEG (and together with Sponsor and AEG, the &quot;Reporting Persons&quot;).</footnote>
        <footnote id="F4">Because of the relationship among the Reporting Persons, the Reporting Persons may be deemed to beneficially own the securities reported herein to the extent of their respective pecuniary interests. Each Reporting Person disclaims beneficial ownership of the securities reported herein, except to the extent of such Reporting Person's pecuniary interest therein, if any.</footnote>
        <footnote id="F5">Pursuant to Rule 16a-1(a)(4) under the Exchange Act, this filing shall not be deemed an admission that the Reporting Persons are, for purposes of Section 16 of the Exchange Act or otherwise, the beneficial owners of any equity securities in excess of their respective pecuniary interests.</footnote>
        <footnote id="F6">The Sponsor forfeited 781,250 Class F Shares to the Issuer for no consideration, which was exempted pursuant to Rule 16b-3(e), in connection with the underwriter's election not to exercise the remaining unused portion of the over-allotment option.</footnote>
    </footnotes>

    <remarks>Exhibit 99.1 Joint Filer Information, incorporated herein by reference.</remarks>

    <ownerSignature>
        <signatureName>By: /s/ Andrew McBride, Attorney-in-Fact for Gores Sponsor III LLC</signatureName>
        <signatureDate>2018-10-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Andrew McBride, Attorney-in-Fact for AEG Holdings, LLC</signatureName>
        <signatureDate>2018-10-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: /s/ Andrew McBride, Attorney-in-Fact for Alec Gores</signatureName>
        <signatureDate>2018-10-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
