Modric, who is the first Croatian to win the Ballon d'Or, beat off competition from former Real Madrid team-mate Ronaldo, who was second, and France's World Cup victor Antoine Griezmann in third place.
Mbappe, who will turn 20 later this month, picked up the consolation prize of the Kopa Trophy for the best young player.
Modric won his third UEFA Champions League in May and played in Croatia to help his team to reach their first World Cup final. "It didn't happen, this is a great feeling to win at least this, and very happy for it".
"It's a big pleasure to be here among all these players".
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Real Madrid midfielder, Luka Modric has disclosed that he will like to end his career at the Santiago Bernabeu. "It's something unique for me", Modric said.
"However, many people and I will see so much more, especially justice. When I dropped back, I was able to read the game better and show my creativity", added Modric.
For the first time in history a Croatian is the proud owner of the most prestigious individual award in football, the Ballon d'or.
He has also won individual medals along the way with the Golden Ball for the best player at the World Cup to the Federation Internationale de Football Association award "The Best" in September.
Modric claimed the coveted individual honour at a ceremony in Paris on Monday - ending the domination of Juventus superstar Ronaldo and Barcelona sensation Messi, who had split the past 10 awards. Messi, who has won Ballon d'Or five times, finished fifth.