'full-grown' is a Modern English compound formed from 'full' + the past participle 'grown' (from the verb 'grow').

'grow' comes from Old English 'grōwan' (to grow); this became Middle English 'growen' and the past participle 'grown', which combined with 'full' to form the compound adjective 'full-grown' in Early Modern English.

Initially it literally described being 'fully filled out' or having 'grown completely'; the meaning has remained essentially the same and denotes full physical development or maturity.