The former Saint-Etienne, Lille and Nice manager took the reins from Mauricio Pochettino last year and steered PSG to Ligue 1 and Trophee des Champions glory.
However, Galtier could not end PSG's hoodoo in the Champions League, as he oversaw a last-16 elimination at the hands of Bayern Munich, and his side only finished one point clear of Lens in Ligue 1.
PSG also confirmed the exits of his assistants Thierry Oleksiak and Joao Sacramento, saying in a statement: "At the end of the 2022-2023 financial year, Paris Saint-Germain and Christophe Galtier have decided to end their first-team coaching contract.
"The Club would like to pay tribute to his professionalism and commitment, which enabled the Rouge & Bleu to win a historic eleventh French Championship title as well as a Champions Trophy.
"The whole of Paris Saint-Germain thanks Christophe Galtier, as well as his assistants Thierry Oleksiak and Joao Sacramento, for the professionalism and commitment shown throughout the season, and wishes them the best for the rest of their careers."
The 56-year-old's reign was also marred by allegations of racism from his time in charge of Nice, with a leaked email purportedly showing Galtier complaining about the number of black and Muslim players in his squad.
Galtier vehemently denies the allegations, but he was recently taken into custody alongside his son - who was released without charge - and he will face trial on December 15 for charges of psychological harassment and discrimination.
Galtier departs PSG with a record of 34 wins, six draws and 10 defeats from 50 matches in charge, and he has been linked with the West Ham United job should the Irons decide to part ways with David Moyes.
Following confirmation of Galtier's dismissal, PSG are expected to announce Enrique as the Frenchman's successor, with a press conference scheduled for 12:45pm UK time.
The ex-Spain and Barcelona head coach has been out of work since departing La Roja for the second time after the World Cup, where he oversaw a last-16 defeat to Morocco on penalties.
Tottenham Hotspur and Chelsea were both linked with moves for Enrique, but the Premier League duo eventually moved for Pochettino and Ange Postecoglou respectively.
Enrique is set to arrive at PSG after the French champions suffered more apparent frustration in their pursuit of long-time target Zinedine Zidane, who supposedly rejected another approach to take charge.
Former Bayern Munich boss Julian Nagelsmann was also said to be the frontrunner at one stage, but talks between the two parties ultimately collapsed, and Les Parisiens have also decided against taking a punt on Bologna's Thiago Motta.
PSG are also expected to confirm the signings of Milan Skriniar, Marco Asensio and Manuel Ugarte this month, while talks to bring Cher Ndour and Lee Kang-in to the Parc des Princes are also believed to be at their final stages.