<?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>0001210707</rptOwnerCik>
            <rptOwnerName>PORCELAIN MICHAEL</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>President &amp; COO</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>1394</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.56</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>107940</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This transaction represents the vesting of 2,846 of the 14,231 restricted stock awards issued to the Reporting Person on August 9, 2016.  The 1,394 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 2,847 will vest on the fifth and final anniversary of grant, assuming continued service as an employee.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Michael D. Porcelain</signatureName>
        <signatureDate>2020-08-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
