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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-08-09</periodOfReport>

    <issuer>
        <issuerCik>0000023197</issuerCik>
        <issuerName>COMTECH TELECOMMUNICATIONS CORP /DE/</issuerName>
        <issuerTradingSymbol>CMTL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001376161</rptOwnerCik>
            <rptOwnerName>Stallone Nancy</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>68 SOUTH SERVICE ROAD, SUITE 230</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MELVILLE</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11747</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>V.P. of Finance and Secretary</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock par value $.10 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2020-08-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>331</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.56</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27049</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This transaction represents the vesting of 973 of the 4,863 restricted stock awards issued to the Reporting Person on August 9, 2016.  The 331 reflected on this table represents the shares withheld to pay the Reporting Person's federal, state and Federal Insurance Contributions Act (&quot;FICA&quot;) tax.  The remaining 973 will vest on the fifth and final anniversary of grant, assuming continued service as an employee.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Nancy Stallone</signatureName>
        <signatureDate>2020-08-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
