'avouch' originates from Anglo-French/Old French, specifically the word 'avoucher' (or Old French 'avouer'), where the prefix 'a-' is a form of 'ad-' (to/toward) and the root related to 'vocare' (to call).

'avouch' changed from Old French 'avoucher'/'avouer' into Middle English forms such as 'avouchen' and eventually became the modern English word 'avouch' and its past 'avouched'.

Initially, it meant 'to call (as a witness) or to summon/acknowledge,' but over time it evolved into its current sense of 'to assert, affirm, or vouch for' (including usage as an acknowledged/admitted form).