Pochettino has been out of work since his sacking from Spurs last November after five years in charge of the north London club.
The Argentine boss spent two years at PSG during his playing career where he won the UEFA Intertoto Cup in 2001.
Tuchel has paid the price after the French champions lost four matches in Ligue 1 this season and enter the winter break in third position in the table, a point behind Lyon and Lille.
The French champions suffered a 1-0 home defeat at the hands of table topping Lyon on Dec. 13 before a goalless draw at Lille on Sunday.
The departure comes four months after Tuchel led the club to their first ever Champions League final where they lost to Bayern Munich in Lisbon.
Former Juventus boss Massimiliano Allegri and ex-Tottenham manager Mauricio Pochettino have been linked with the position in recent months.
Tuchel was appointed on a two-year contract in 2018, replacing Unai Emery, and won the Ligue 1 title in his first campaign before claiming a domestic Treble in his second as well as reaching the Champions League final.
However, his third season in Paris was overshadowed by a disagreement with PSG sporting director Leonardo over player recruitment.
In October, Tuchel publicly criticised Leonardo and said: “We lose too many players on free transfers. It is too, too much. We cannot ask this squad the same thing as we did last season.”
Leonardo responded the following day, after PSG’s 6-1 win against Angers in Ligue 1: “I didn’t like his comments, the club didn’t like them either.”
“We have to understand the moment we are going through. If someone is not happy, it is easy — we can talk. But if you decide to stay, you have to respect the people above you.”
Thiago Silva, Eric Maxim Choupo-Moting, Thomas Meunier, Edinson Cavani, Tanguy Kouassi and Adil Aouchiche all left PSG over the summer, although they did sign Alessandro Florenzi, Moise Kean and Danilo Pereira on loan and Rafinha on a free transfer.
Tuchel parted ways with Borussia Dortmund in May 2017 amid reported disagreements with the club hierarchy, despite guiding the club to the DFB Pokal title three days earlier.
PSG return to action when they face a trip to Saint-Etienne on Jan. 6.