The Uruguay international beat off competition from fellow nominees Lyon striker Alexandre Lacazette, Monaco's Bernardo Silva and Paris team-mate Marco Verratti.
It is the seventh time a Paris Saint-Germain player has won the award (David Ginola 1993-1994, Vincent Guérin 1994-1995, Marco Simone 1997-1998, Zlatan Ibrahimovic 2012-2013, 2013-2014 and 2015-2016, and the Paris number 9 2016-2017), a record.
"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," Cavani told beIN SPORTS 1. "I would also like to thank my colleagues who voted for me."
The full UNFP Trophy list
Ligue 1 Player of the Year: Cavani, who succeeds Ibrahimovic
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)
Women's D1 Player of the Year: Dzsenifer Marozsan (Olympique lyonnais)
Women's D1 Revelation of the Year: Sakina Karchaoui (Montpellier Hérault)
Ligue 1 Referee of the Year: Ruddy Buquet
Ligue 2 Referee of the Year: Alexandre Castro
Best French referee on the international scene: Clément Turpin
Lifetime achievement: Raymond Kopa