The PSG forward beat French stars Karim Benzema and Kylian Mbappe to win the prize for the second time.
He led Argentina to World Cup glory in Qatar and scored 27 goals in 49 appearances for club and country during the 2021-22 season.
Messi 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 teammates 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."
Argentina manager Lionel Scaloni was named as men's coach of the year after leading the South American nation to a third World Cup win and beat Pep Guardiola and Carlo Ancelotti to the prize.
Argentine Emiliano Martinez was recognised as the best men's goalkeeper for his heroics in Qatar and paid tribute to his parents for helping him realise his dream.
He 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."
On the women's side, Barcelona's Alexia Putellas was named as player of the year and there were also honours for coach Sarina Wiegman and goalkeeper Mary Earps after they helped England to glory at Euro 2022.