The Uruguay striker netted his 157th goal for the club at home to Montpellier on Saturday in their 4-0 win.
Cavani arrived at Parc des Princes from Napoli for around €64million in 2013.
He was booked by referee Frank Schneider for taking his shirt off in celebration, at setting a new benchmark tally in his 229th appearance across all competitions.
“Writing my name into history with this club, this team and these supporters, it is magnificent,” Cavani told Canal+.
“Sincerely, I am very happy to have scored here.
“I hope to continue and to be able to give even more to PSG. This common love with the fans is truly a thing of beauty – it moves me.
“We must make the most of it. It is not often in life that you receive this much affection. I am pleased to be here. I hope that I will stay for many more years.”