Pogba, whose contract was due to run until June 2027, has struggled to re-establish himself since returning from a doping ban that kept him out of action for more than two years.
Monaco said they had reached an agreement with the 33-year-old midfielder after determining that the objectives outlined when he joined the club had not been fully achieved.
"I would like to thank the President and the management, my teammates, all the staff and all the fans who believed in me. Representing this Club and the Principality was an incredible experience," Pogba said in a statement.
"AS Monaco is an exceptional club and, even if I haven't played as many games as I hoped, I will always remain grateful to have had the opportunity to wear its colours. Daghe Munegu!"
The 2018 World Cup winner made only six appearances for Monaco, including one start.
Pogba, the former Manchester United and Juventus player, is currently recovering from a thigh injury after recently returning from a knee problem.