Both stalwarts will be out of contract later this summer and will now have to find new clubs.
While PSG have been crowned champions in France after the coronavirus pandemic led to a curtailment of the season, Thomas Tuchel’s men are still alive in the UEFA Champions League, which is planned to resume in August, and they also have to take on Saint Etienne in the Coupe de la Ligue final and Olympique Lyon in the Coupe de France decider.
Thiago Silva joined PSG from AC Milan in the summer of 2012, winning seven Ligue 1 titles while Cavani moved to the Parc des Princes from Napoli in 2013 and has won six top flight trophies, with his 200 goals a club record.
PSG sporting director Leonardo confirmed the pair’s departure in an interview with Journal de Dimanche.
"It was a really difficult decision to take. [Thiago Silva and Edinson Cavani] are players who have had a big impact on this club's history," said Leandro.
"You always wonder if you should carry on down the same path together or if it's better to avoid a scenario where you've stayed for one year too many.
"It's been such a wonderful journey, but we're coming to the end. We had to make a logical decision, both in financial terms and also considering the next generation of players coming through.
"Maybe it's the wrong decision, I don't know. There's never a perfect moment. The Champions League is still on the agenda and the plan is to remain in the competition with them until the end of August."
Cavani, 33, has attracted interest from Atletico Madrid while 35-year-old Silva has been linked with a return to Milan.