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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-08-04</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001195452</rptOwnerCik>
            <rptOwnerName>PAUL ROBERT G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>20 VIA TIBERIUS WAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HENDERSON</rptOwnerCity>
            <rptOwnerState>NV</rptOwnerState>
            <rptOwnerZipCode>89011</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock Par Value $0.10 Per Share</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <transactionDate>
                <value>2020-08-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7195</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26907</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock awards were granted under the Company's 2000 Stock Incentive Plan, and represent the right to receive one share of common stock of Comtech Telecommunications Corp. upon vesting.</footnote>
        <footnote id="F2">Generally, the restricted stock awards will vest in installments over a five year period, at a rate of 20% on the first through fifth anniversaries of grant, assuming continued service as a director. Shares of common stock corresponding to vested awards will be delivered to the reporting person within 30 days of vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Robert G. Paul</signatureName>
        <signatureDate>2020-08-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
