'illegitimately-approved' originates from Modern English as a compound of 'illegitimately' and 'approved'. 'illegitimately' ultimately derives from Latin 'illegitimus' (via Old French and Middle English), where the prefix 'il-' meant 'not' and 'legitimus' meant 'lawful'; 'approved' originates from Latin 'approbare', where the prefix 'ad-/ap-' meant 'to/toward' and 'probare' meant 'to test, to prove, to approve'.

'illegitimus' changed into Old French and Middle English forms (e.g. Middle English 'illegitimat(e)') and became English 'illegitimate' with the adverbial form 'illegitimately'; Latin 'approbare' became Old French 'aprover' and Middle English 'aprouven', eventually yielding modern English 'approve'. The compound adjective formed in Modern English by combining an adverb with a past participle (illegitimately + approved).

Initially, the roots meant 'not lawful' (illegitimus) and 'to prove or declare good' (approbare). Over time, combining them produced the specific sense 'approved by illegitimate or improper means'.