He left Nice last month after guiding them to fifth in Ligue 1 and a runner-up finish in the French Cup last season.
The 55-year-old, who led Lille to the Ligue 1 title in 2021, is PSG’s seventh coach since the Qatari takeover of the club in 2011.
“I am delighted to join Paris Saint-Germain, I would like to thank the Chairman Nasser Al-Khelaifi, (football advisor) Luis Campos and the club for their confidence in me,” he said.
“I am fully aware of the responsibilities involved to coach this extraordinary team, which is one of the most competitive and spectacular squads in Europe.”
Galtier is one of only two managers to stop PSG winning Ligue 1 in the past decade, along with Leonardo Jardim’s Monaco in 2016-17.
He resigned after leading Lille to that unexpected title success in May 2021 before spending 12 months at Nice. He previously managed Saint-Etienne.
Pochettino, 50, leaves PSG after just 18 months in charge having guided them to a record-equalling 10th French title last season, his first league success as a manager.
The exit of the former Tottenham boss had been expected for almost a month now – but was only announced shortly before Galtier’s appointment was confirmed yesterday.
A club statement read: “Paris Saint-Germain confirm that Mauricio Pochettino has ended his role at the club.
“The club would like to thank Mauricio Pochettino and his staff for their work and wish them the best for the future.”
The former PSG defender oversaw an unbeaten home record in the league this season, ending the campaign with 16 wins in 19 games.
PSG regained the title but their last-16 Champions League exit – with Lionel Messi in the team – was seen as a major failure.