The pair are both out of contract with the Ligue 1 club in June but will stay on until the season is over.
PSG are through the Champions League quarter-finals with the competition expected to not be over until August.
Owing to the coronavirus pandemic with PSG handed the title, the Ligue 1 season was cut short.
Sporting director Leonardo said: “Taking a decision was truly difficult. [Thiago Silva and Edinson Cavani] are players who have had a tremendous influence on the history of this club. You ‘re always wondering if you should take the same direction together or if it’s easier to avoid a situation where you’ve kept too long for one year.
“It was such a fun trip but we’re coming to the door. Both financially and considering the next generation of players coming through, we needed to make a rational decision. It’s probably the wrong decision, I don’t know. There never is a perfect moment here. The Champions League is still on the agenda and the plan is to stay with them until the end of August in the competition, he added.
Cavani, 33, is PSG’s all-time lead scorer after joining Napoli, with 200 goals in seven seasons.