The 35-year-old beat French forwards Kylian Mbappe and Karim Benzema to the prize.
Messi captained Argentina to World Cup glory in Qatar, and scored 27 goals in 49 games for club and country in 2021-22.
Barcelona's Alexia Putellas was named women's player of the year.
Messi, who won the award for a second time, said: "It's amazing. It's been a tremendous year and it's an honour for me to be here and win this award. Without my team-mates I wouldn't be here.
"I achieved the dream I had been hoping for for so long. Very few people can achieve that and I have been lucky to do so."
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 guided 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 leading 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 best men's goalkeeper, while England's Mary Earps won the women's award.
Martinez, 30, helped his country win the World Cup, saving four penalties along the way including in the shootout victory against France in the final.
Collecting his award, Martinez said: "They always ask me who my idols are or who I watched when I was a kid… watching my mum clean buildings for eight or nine hours and watching my dad work. They are my idols."
Earps, who plays for Manchester United in the Women's Super League, started all six of England's games at Euro 2022 as they won the competition.
She said: "For anyone who has been in a dark place, just know there is light at the end of the tunnel, so keep going. You can achieve anything that you set your mind to."
Amputee footballer Marcin Oleksy, of Polish side Warta Poznan, won the Fifa Puskas award for the best goal of the year. He sent a stunning overhead volley against Stal Rzeszow flying into the back of the net with the help of his crutches.
Recipient of the fair play award was Luka Lochoshvili, who held the tongue of his opponent, Georg Teigl, to save his life after the midfielder had fallen unconscious.
Fifpro men's world XI: Thibaut Courtois; Achraf Hakimi, Virgil van Dijk, Joao Cancelo; Kevin De Bruyne, Luka Modric, Casemiro; Lionel Messi, Erling Haaland, Karim Benzema, Kylian Mbappe.
The Best men's player: Lionel Messi
The Best women's player: Alexia Putellas
The Best men's goalkeeper: Emiliano Martinez
The Best women's goalkeeper: Mary Earps
The Best men's coach: Lionel Scaloni
The Best women's coach: Sarina Wiegman
The Best Puskas award: Marcin Oleksy
The Best fan award: Argentina fans
The Best fair play award: Luka Lochoshvili