Messi won the 2022 World Cup with Argentina in December -- the country's first in 36 years -- ending his wait for the only major honour to have eluded him in his career.
"It's amazing. It was a tremendous year and it is an honour for me to be here tonight and win this award," said Messi, who sat next to Mbappe throughout the ceremony at the Salle Pleyel.
Monday's award was Messi's second FIFA The Best title, his first coming in 2019. He has also won a record seven Ballon d'Or awards.
"I want to express my thanks to [coach Lionel] Scaloni and my teammates; without them I would not be here," Messi added.
"I achieved a dream I had been hoping for so long and finally I achieved it. It's a dream for any player; very few people can achieve that and I was lucky enough to do so."
Messi scored seven goals at the World Cup in Qatar -- including a brace in the thrilling 3-3 final victory on penalties -- finishing one behind Golden Boot winner Mbappe.
Messi has scored 16 goals in 27 games in all competitions this season, as well as registering 14 assists, as he chases his second Ligue 1 title in two years at PSG.
Barcelona president Joan Laporta congratulated Lionel Messi on winning. After Barca congratulated their club's all-time goalscorer for his latest individual trophy, Laporta said on Twitter: "Congratulations Leo Messi! A new and well-deserved recognition of a legendary career. The Culers will always be proud that you are part of our history."
Barcelona's Alexia Putellas won the Best FIFA Women's award for the second year running, while Argentina's Scaloni and Emiliano Martinez got the honours for top men's coach and goalkeeper, respectively.
Polish amputee Marcin Oleksy won the Puskas prize for best goal of the year for a spectacular acrobatic volley with Warta Poznan against Stal Rzeszow.
Information from Reuters was used in this story.