The award has been given out annually since 1956 through France Football Magazine to the player of the year as decided by a panel of football journalists.
"As a kid we all have dreams".
"My son, I am the happiest and proudest father in the world", he said.
"I just want to thank all those who helped me to be here tonight, I thank my team-mates, my coaches, the staff and Real Madrid, all those who work there, the coaches and team-mates in the national team, the ones who voted for me and my family, which allows me to blossom as a person".
The 19-year-old Mbappe - the youngest player to score in a World Cup final - also won the Raymond Kopa Trophy awarded to the best young player. Brazil star Neymar was third previous year but only 12th this time.
Lyon's Ada Hegerberg became the first recipient of the Women's Ballon d'Or award.
The win was slightly overshadowed when the host DJ Martin Solveig asked Hegerberg to twerk on stage in celebration. The Portuguese ended up as runner-up, while Messi was not even in the top three.
Real Madrid's Croatian midfielder Luka Modric kisses the trophy after receiving the 2018 FIFA Men's Ballon d'Or award for best player of the year during the 2018 FIFA Ballon d'Or award ceremony at the Grand Palais in Paris on December 3, 2018.
Hegerberg is a three-time Women's Champions League victor with Olympic Lyonnais and scored a tournament-record 15 times last season.
Harry Kane's impressive season along with his Golden Boot award at the World Cup earnt him first prize on the South Pacific Island of Vanuatu.
With the result widely known even before the ceremony, World Cup 2018 victor Griezmann said on his way into the building: "It's a pity that a Frenchman didn't win".
Monday was a big day for many people in the football galaxy. I didn't really think about it at the time to be honest.