'variously-leaved' originates from Modern English as a compound of 'variously' and 'leaved'; 'variously' ultimately comes from Latin 'varius' (via Old French/ Middle English) where 'varius' meant 'different, changing', and 'leaved' derives from Old English 'lēaf' meaning 'leaf'.

'variously' developed from Latin 'varius' → Old French 'varie'/'various' → Middle English 'various' → adverbial form 'variously'; 'leaved' comes from Old English 'lēaf' → Middle English 'leaf' with the adjectival suffix '-ed', producing forms like 'leaved' in Modern English, and the two elements combined in descriptive botanical compounds like 'variously-leaved'.

Initially the component roots meant 'different' (varius) and 'leaf' (lēaf); combined in Modern English the compound has kept the literal descriptive meaning 'having leaves of various kinds', largely unchanged in botanical usage.