'reverse' originates from Old French 'revers' and ultimately from Latin 'revertere', where 're-' meant 'back' and 'vertere' meant 'to turn'; 'order' originates from Latin 'ordo' meaning 'row, rank, arrangement'.

'reverse' passed into Middle English via Old French as 'revers' and later took the modern form 'reverse'; 'order' came into English via Old French 'ordre' from Latin 'ordo, ordinis' and developed into the Modern English 'order'.

Each component kept much of its original sense: 'reverse' originally meant 'to turn back' and 'order' meant 'an arrangement'; combined as a phrase they came to mean 'an arrangement turned back' or 'the opposite arrangement'.