The Uruguay international scored 49 goals in 48 games across all competitions this season - which includes 35 strikes in as many Ligue 1 appearances for Unai Emery's side.
The former Napoli hit-man greatly benefited from the departure of the previous winner of the award Zlatan Ibrahimovic, as Les Parisiens main attacking outlet.
Lyon striker Alexandre Lacazette, Monaco's Bernardo Silva and team-mate Marco Verratti were the other nominees this season.
"Firstly, I'd like to thank my team-mates, who have given me the possibliity to be here this evening, as well as all the people who work at Paris Saint-Germain," he told beIN SPORTS 1. "I would also like to thank my colleagues who voted for me."
Leonardo Jardim walked away with the coach of the Year award after leading a young exciting Les Monégasques to the brink of the title - ending PSG's dominance over the division.
Their goalkeeper Danijel Subasic and wonderkid Kylian Mbappe were also rewarded for their efforts this season. While former Manchester United outcast Memphis Depay won goal of the season.
Former Tottenham Hotspur trainee John Bostock picked up the Ligue 2 Player of the Year award for his role with promotion chasing RC Lens - as the driving force in their midfield.
The full UNFP Trophy list:
Ligue 1 Player of the Year: Edinson Cavani (PSG)
Coach of the Year: Leonardo Jardim (AS Monaco)
Goalkeeper of the Year: Danijel Subasic (AS Monaco)
Young Player of the Year: Kylian Mbappé (AS Monaco)
Goal of the Season: Memphis Depay (Olympique lyonnais)
Best French player abroad: N'Golo Kanté (Chelsea FC)
Ligue 2 Player of the Year: John Bostock (RC Lens)
Ligue 2 Goalkeeper of the Year: Nicolas Douchez (RC Lens)
Ligue 2 Coach of the Year: Bernard Blaquart (Nîmes Olympique)