Pochettino has been given the reigns on an initial one-and-a-half-year contract with the option to extend for a further year.
The 48-year-old had been out of work since leaving Tottenham Hotspur in November 2019.
"I am really happy and honoured to become the new coach of Paris Saint-Germain," said Pochettino, who played for PSG from 2001 to 2003. "I would like to thank the club's management for the trust they have placed in me.
"As you know, this club has always held a special place in my heart. I have wonderful memories, especially of the unique atmosphere of the Parc des Princes. I return to the club today with a lot of ambition and humility, and am eager to work with some of the world's most talented players.
"This team has fantastic potential and my staff and I will do everything we can to get the best for Paris Saint-Germain in all competitions. We will also do our utmost to give our team the combative and attacking playing identity that Parisian fans have always loved."
Club chairman and CEO Nasser Al-Khelaifi said: "We are very pleased to welcome Mauricio Pochettino as first team coach.
"I am proud to see our former captain returning to Paris Saint-Germain, as the club has always remained his home.
"The return of Mauricio fits perfectly with our ambitions and it will be another exciting chapter for the club and one I am positive the fans will enjoy."
PSG are third in the French top flight, having lost four of their 17 games and have been paired with Barcelona in the last 16 of the Champions League which resumes in February.
