The 26-year-old Donnarumma joined PSG from AC Milan in 2021 and was a key factor in their first Champions League triumph earlier this year as part of a treble, but then fell out of favour at the club.
PSG manager Luis Enrique dropped him from the Uefa Super Cup squad after the arrival of goalkeeper Lucas Chevalier.
Donnarumma was crucial in PSG's Champions League triumph, saving penalties from Darwin Nunez and Curtis Jones to knock Liverpool out in a shootout in the last 16. He kept a clean sheet in the 5-0 win over Inter Milan in the final in May.
The next month, the Italian helped PSG reach the 2025 Club World Cup final, where they were defeated 3-0 by Chelsea.
The day after Donnarumma was left out of the Super Cup squad, the Italian announced he would leave the club, saying he was "disappointed and disheartened" by the decision to freeze him out.
"I am joining a squad packed with world-class talent and a team led by one of the greatest managers in the history of football in Pep Guardiola. This is a club every player in world football would love to join," Donnarumma said.