Mauricio Pochettino (left) had never won a major trophy before taking over at PSG
Galtier has signed a two-year deal until the summer of 2024.
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 on Tuesday.
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.
They squandered a 2-0 aggregate lead in the Champions League against eventual champions Real Madrid to cast a serious question mark over the Argentine's future.
It was the first time Les Parisiens, who reached the semi-finals in 2021 and were the beaten finalists in 2020, had lost a Champions League away game after leading at half-time since 2001.
Pochettino was sacked by Spurs in November 2019 after five years in charge of the Premier League club, months after leading them to the 2019 Champions League final.
After taking charge of PSG in January last year, they finished second in Ligue 1 behind Galtier's Lille and were beaten in that year's Champions League semi-finals by Manchester City.
However, they won the Coupe de France and the Trophee des Champions, which were the first trophies of Pochettino's managerial career.
The former Argentina defender began his managerial career at Espanyol and spent 18 months at Southampton before joining Tottenham in May 2014.
-- Courtesy of BBC Sport