'opposite-sign' originates from modern English as a compound formed from 'opposite' and 'sign'. 'opposite' ultimately comes from Latin 'oppositus' (via Old French/Latin), where 'oppositus' meant 'placed against'; 'sign' originates from Latin 'signum', where it meant 'mark' or 'token'.

'opposite' passed into Middle English from Old French and Latin (Latin 'oppositus'); 'sign' passed into Middle English from Old French 'signe' and Latin 'signum'. The hyphenated technical compound 'opposite-sign' is a relatively recent English formation used particularly in mathematics and the physical sciences.

Initially, 'opposite' and 'sign' had their separate senses ('placed against' and 'mark' respectively); combined into 'opposite-sign' the compound gained the specialized meaning 'having an opposite algebraic sign' used in technical contexts.