<?xml version="1.0"?>
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    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001289236</issuerCik>
        <issuerName>BioMed Realty Trust Inc</issuerName>
        <issuerTradingSymbol>BMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001316256</rptOwnerCik>
            <rptOwnerName>Lubushkin Greg</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>17190 BERNARDO CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92128</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                </transactionShares>
                <transactionPricePerShare>
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        </nonDerivativeTransaction>
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    <derivativeTable>
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            <securityTitle>
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            <transactionAmounts>
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                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
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                <footnoteId id="F5"/>
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            <expirationDate>
                <footnoteId id="F5"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <underlyingSecurityShares>
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                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Units 2014</value>
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                <value>2015-12-31</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>53300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <expirationDate>
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                <underlyingSecurityShares>
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                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Units 2015</value>
            </securityTitle>
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            <transactionDate>
                <value>2015-12-31</value>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
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                <value></value>
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                    <value>44840</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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    <footnotes>
        <footnote id="F1">Represents earn-out of previously awarded performance units granted in January 2013.</footnote>
        <footnote id="F2">Represents earn-out of previously awarded performance units granted in January 2014.</footnote>
        <footnote id="F3">Represents earn-out of previously awarded performance units granted in January 2015.</footnote>
        <footnote id="F4">Represents payment of tax liability by the forfeiture of shares of common stock to the company incident to the vesting of the reporting person's performance units and restricted stock.</footnote>
        <footnote id="F5">Each performance unit represents a contingent right to receive one share of the company's common stock. 24,864 performance units vested and 124 performance units were forfeited on December 31, 2015, based on the company's total stockholder return performance relative to a selected peer group for the three years ended December 31, 2015.</footnote>
        <footnote id="F6">Each performance unit represents a contingent right to receive one share of the company's common stock. All performance units vested on December 31, 2015, based on the company's total stockholder return performance relative to a selected peer group for the two years ended December 31, 2015.</footnote>
        <footnote id="F7">Each performance unit represents a contingent right to receive one share of the company's common stock. All performance units vested on December 31, 2015, based on the company's total stockholder return performance relative to a selected peer group for the one year ended December 31, 2015.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Jonathan P. Klassen, Attorney-In-Fact</signatureName>
        <signatureDate>2016-01-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
