Donnarumma's replacement, 25-year-old Mike Maignan, has been rumored to the club for some time.
He joins from Lille who sensationally won the league title before PSG.
Maignan, who is part of France's European squad, has signed a five-year contract, Milan announces.
Donnarumma has, among other things, been linked with a move to league rival Juventus.