The Paris Saint-Germain star was one of the stars in France's triumphant World Cup campaign as Didier Deschamps' squad emerged victorious at the Russia 2018 tournament.
With 32 goals in 56 games in all competitions for club and country in 2018, Mbappe beat fellow nominees including Liverpool full-back Trent Alexander-Arnold and Borussia Dortmund's United States international Christian Pulisic.
"I am very happy to receive this award," Mbappe said.
"This rewards a great year, which I realised thanks to all my team-mates at PSG and with the national team.
"I will never forget the adventure of the World Cup. It's a good time to thank them. And it's an extra motivation to keep working.
"My next goal? It is to win everything. It will be with hard work and help from my team-mates."
Mbappe, the top goalscorer in Europe's top-five leagues this season with 12 strikes, was the only player on the shortlist for the Kopa Trophy who was also listed among the nominees for the Ballon d'Or prize.
