'officially-approved' is a compound formed from the adverb 'officially' (from 'official') and the past participle 'approved' (from 'approve'). 'official' originates from Latin, specifically the Medieval Latin word 'officialis', where 'officium' meant 'service' or 'duty'; 'approve' originates from Latin, specifically the word 'approbare', where the prefix 'ad-' meant 'to' and 'probare' meant 'to test' or 'to demonstrate good/fit'.

'official' passed into English via Old French/Anglo-Norman and Middle English from Medieval Latin 'officialis'; 'approve' passed into English via Old French 'aprover' (or 'aprover' in Medieval French) from Latin 'approbare', and the past participle forms (approved) came to be used adjectivally (e.g. 'approved plan'). The modern compound/phrase 'officially approved' arose by combining the adverbial form with the participle to indicate formal authorization.

Initially the components meant 'related to duty or service' (official) and 'to demonstrate as good or acceptable' (approve); over time the combined phrase came to mean 'formally authorized or sanctioned by an authority'.