The France forward is the only player to win the award four times, beating the record he shared with Zlatan Ibrahimovic.
"I want to thank the players, the staff, all the people working in the shadows," said 24-year-old Mbappe.
"I've always wanted to leave a mark. I did not expect to win so much so early but I'm happy to make history in my country."
Mbappe has a contract with PSG until 2024 with an option to extend it by a further year.
"I'm happy and I'll be here next season," he said, not giving a clue on whether he would stay at the club until 2025.
PSG wrapped up the title with one game to spare after a 1-1 draw at Racing Strasbourg on Saturday.
Franck Haise was named best coach of the season after leading Lens to second place, which will see the northern club play in the Champions League for the first time in 21 years.
"It's the story of three seasons ... those who are not in this adventure anymore, I don't forget you," said Haise, who took over the first team when they were in Ligue 2 in 2020. What we've been through is unforgettable."
Lens also had four players in the team of the season - Brice Samba, Kevin Danso, Seko Fofana and Lois Openda - with Samba being named best goalkeeper.
PSG also had four players selected - forwards Mbappe and Lionel Messi plus fullbacks Nuno Mendes and Achraf Hakimi.
