According to international media reports, 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.