After having the 20-year-old left-back on loan last campaign, the club have now negotiated a unique deal to bring him back to Molineux.
Wolves will pay £10million for him while Angers have a 50 per cent sell-on.
However, Wolves have a buyout clause should they wish to remove that sell-on at a later date.
Ait-Nouri's signing is expected to be confirmed by the club in the coming days.
The Frenchman made 24 appearances in gold and black last term, scoring once, becoming a regular presence at the back thanks to promising displays and injuries to Jonny Castro Otto and Fernando Marcal.
It is thought he will have to isolate ahead of joining Bruno Lage's squad for pre-season.
Ait-Nouri's permanent arrival is set to allow Ruben Vinagre to leave after four years with the club, with Sporting Lisbon close to securing his services.
Meanwhile, Wolves have announced season tickets for the 2021/22 campaign will go on sale on Monday.