The pair are both out of contract with the Ligue 1 club in June however will stay on until the season is finished.
PSG are through the Champions League quarter-finals with the opposition expected to not be over until August.
Attributable to the coronavirus pandemic with PSG handed the title, the Ligue 1 season was cut short.
Brandishing director Leonardo said: “Taking a choice was really troublesome. [Thiago Silva and Edinson Cavani] are players who have had a huge impact on the history of this club. You ‘re always thinking about whether you should take the same bearing together or if it’s easier to avoid a situation where you’ve kept too long for one year.
“It was such a great excursion yet we’re going to the entryway. Both financially and considering the up and coming generation of players coming through, we expected to make a rational choice. It’s probably an inappropriate choice, I don’t have the foggiest idea. There never is an ideal second here. The Champions League is still on the agenda and the plan is to stay with them until the finish of August in the opposition, he added.
Cavani, 33, is PSG’s all-time lead scorer after joining Napoli, with 200 goals in seven seasons.
Silva, 35 has won 21 trophies in the French capital during his eight seasons. He is the captain of the club.