'approvedly' ultimately derives from Latin via English word formation: Latin 'approbare' (from 'ad-' + 'probare'), where 'ad-' meant 'to' and 'probare' meant 'to test or prove', leading to English 'approve' + the adverbial suffix '-ly'.

'approve' changed from Old French 'aprover' and Middle English 'aprouven' into modern English 'approve'; the past participle/adjective 'approved' then took the suffix '-ly' to form the adverb 'approvedly'.

Initially, the Latin root meant 'to test or prove'; over time the meaning shifted to 'to give assent or sanction', and 'approvedly' came to mean 'in an approved or sanctioned manner'.