He was a free agent after leaving AC Milan, where he broke into the side as a 16-year-old and made 251 appearances.
Five years ago, Donnarumma became the youngest goalie to play for Italy at 17 years and 189 days when he featured against France.
PSG lost the French title to Lille last season and has strengthened its squad in a bid to persuade star striker Kylian Mbappe to agree a new contract.
PSG has signed veteran defender Sergio Ramos on a free transfer after he played 16 years for Spanish giant Real Madrid and bought right back Achraf Hakimi from Italian champion Inter Milan for a reported fee of 60 million euros ($71 million).
More AP soccer: https://apnews.com/hub/soccer and https://twitter.com/AP_Sports