Pochettino leaves the Parc des Princes after 18 months in charge, paying the price for PSG's failures in Europe.
The former Tottenham Hotspurs boss led PSG to the semi-finals of Europe's premier club competition in the 2020/2021 season but the Parisians bowed out at the round of 16 stage last term, losing to eventual winners Real Madrid.
But Pochettino also led PSG to reclaim the Ligue 1 title from Lille in his only full season in charge.
PSG said in a statement on Twitter: "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."
Galtier comes in as an immediate replacement for Pochettino, signing a two-year contract.
The 55-year-old led Lille to the Ligue 1 title in the 2020/2021 season before leaving for Nice last term, leading them to a fifth place finish.
"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," Galtier said at his presentation on Tuesday.
"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."
He added: "I'm ready, I accept the responsibilities and I'm capable."
"Alone it will be difficult. We will be a lot stronger working together. I will understand if there is any scepticism but I am relishing the challenge."
