The Italian shot-stopper fell out of favour with PSG manager Luis Enrique despite helping the club win Ligue 1 and the Champions League last season.
He joins City as a direct replacement for the outgoing Ederson, who joined Fenerbahce on Tuesday.
Donnarumma arrives as a four-time Ligue 1 winner and three-time goalkeeper of the season (twice with PSG and once with AC Milan).
“To have signed for Manchester City is such a special and proud moment for me,” Donnarumma said in the official announcement on City's website.
“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.
“I am very excited for what lies ahead and can promise that I will give absolutely everything to try and help the Club achieve even more success,” he added.
“Gianluigi’s pedigree, quality and record speak for themselves, and we are all absolutely thrilled he has joined us here at City,” said City's Director of Football, Hugo Viana.
“There is no doubt Gianluigi will bring further quality and depth to our top-class goalkeeping department.
“Everyone here is very excited to welcome Gianluigi to Manchester City, and we wish him all the very best during his time here with us,” Viana concluded.
The Italian is approaching his 10th season in senior football despite still only being 26 years old, and will compete with James Trafford for the number one spot at Manchester City.