The seven-time Ballon d'Or winner beat French forwards Kylian Mbappe and Karim Benzema to the award.
Messi, 35, helped Argentina win the 2022 World Cup in Qatar, scoring 27 goals in 49 games for club and country in 2021-22.
Barcelona's Alexia Putellas was named women's player of the year.
At the ceremony in Paris, Lionel Scaloni, who led Argentina to their third World Cup title, was named men's coach of the year.
Scaloni beat Pep Guardiola - who led Manchester City to a sixth Premier League title - and Real Madrid's Champions League-winning boss Carlo Ancelotti to the honour.
England manager Sarina Wiegman was named women's coach of the year after guiding the Lionesses to European Championship glory on home soil last year, the team's first major trophy.
Aston Villa and Argentina's Emiliano Martinez was recognised as the leading men's goalkeeper.
The 30-year-old helped his country win the World Cup, saving four penalties along the way including in the shootout victory against France in the final.
Amputee footballer Marcin Oleksy of Polish side Warta Poznan won the Fifa Puskas award for the best goal in world football for his stunning strike against Stal Rzeszow, when he sent a powerful overhead volley into the back of the net with the help of his crutches.