Maxwell has won four Ligue 1 titles since joining the French giants from Barcelona.
“It’s a great pleasure to extend my contract with Paris Saint-Germain,” Maxwell said in a statement.
“I get along very well with the players and everyone at the club. The story goes on and I am extremely happy.
“I hope to take the team forward, think about the squad first. We will keep on being competitive, try to go as far as possible in every the competitions. We want to win as many titles as possible, the club deserves it.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.