PSG announced on its website that former Tottenham manager Pochettino had signed a contract until June 30, 2022 with an option for an additional year.
The 48-year-old Argentine was the only name in the frame to take over at the club where he played from 2001 to 2003 after PSG abruptly ended Tuchel's involvement on December 24, reportedly for comments viewed as critical of the Qatari owners.
"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," Pochettino said in the PSG statement.
"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," Pochettino said, adding he would do his utmost "to give our team the combative and attacking playing identity that Parisian fans have always loved."
His priority will be to sate the Qatari-backed club's quest for Champions League glory.
Tuchel, who oversaw the club's first ever Champions League final appearance last season, guided Neymar and company into the knock-out stages this season before being axed.
Pochettino's first major test will be the Champions League last-16 away leg at Barcelona next month.
Pochettino will take charge of his first match next Saturday at Saint-Etienne as Ligue 1 resumes after the winter break with PSG one point off the leaders in third.
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