The news had been widely expected since the departure of Tuchel, who was relieved of his duties in December despite leading PSG to the Ligue 1 title and the Champions League final last season.
The 48-year-old Argentinian has been out of work since being sacked by Tottenham Hotspur in November 2019, the season after he led the north London club to its first Champions League final.
Pochettino, who has also managed Espanyol and Southampton, made 95 appearances for PSG between 2001 and 2003 during his playing career.
He has signed a contract with the Parisian giants until the summer of 2022 with the option of a further year.
“I am really happy and honored to become the new coach of Paris St Germain.
“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,” he told the club’s official website.
“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.”
Tuchel paid the price for PSG’s slow start to the French domestic season, lying third in the standings, but reports also circulated that he angered the team’s Qatari owners by critical comments he made in an interview.
PSG chairman and chief executive Nasser Al-Khelaifi said on the club’s official website: “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.
“With the appointment of Mauricio Pochettino, Paris St Germain are committed to continue to build and move the club forward over the coming years.”
Pochettino cemented his reputation as a leading manager at Tottenham, guiding the side to four straight top four spots in the English Premier League and the 2019 Champions League final, losing 2-0 to Liverpool.
It was the start of a decline in fortunes for Tottenham, which was sliding down the league when Jose Mourinho replaced him.
Pochettino, an uncompromising defender in his playing days, has a reputation for bringing on young players, including Dele Alli, the England midfielder currently out of favor at Tottenham and already being linked with a move to PSG to reunite with Pochettino.
Pochettino’s immediate priority will be to restore dominance in Ligue 1, trailing Lyon and Lille by a point, followed by a crunch Champions League last 16 tie against Barcelona.