France men's international Dembele, who helped PSG to a treble including their first Champions League title, said on stage in Doha: "It has been a fantastic year individually and collectively."
Bonmati picked up the women's award for the third straight year despite Spain losing to England in the Euro 2025 final and Barcelona being beaten in the Champions League final by Arsenal.
"I will enjoy it," she said from Barcelona, where she is recovering from a broken leg.
Coaches of the year were PSG's Luis Enrique and England boss Sarina Wiegman, who took the award for the fifth time. Neither attended though Enrique is in Qatar ahead of Wednesday's Intercontinental Cup final between PSG and Flamengo.
Italy goalkeeper Gianluigi Donnarumma, now of Manchester City, scooped the FIFA Best male goalkeeper award having starred for previous club PSG.
England and Chelsea goalkeeper Hannah Hampton was named Best female keeper.
All six won the equivalent awards at the rival Ballon d'Or ceremony in September.
Mexican player Lizbeth Ovalle won the Marta award for the best women's goal after her spectacular "reverse scorpion kick" for Tigres against Chivas Guadalajara. She has since moved to Orlando Pride.
The Puskas award for best men's goal went to Santiago Montiel for his overhead kick from outside the box for Club Atletico Independiente in Argentina.
Jahn Regensburg team doctor Andreas Harlass-Neuking won the FIFA Fair Play Award for saving the life of a fan at a German second-division game in April.
The fan award went to supporters of Iraqi side Zakho SC, who threw thousands of stuffed toys onto the pitch from the stands in May. They were then gathered and donated to sick youngsters.
FIFA said 16 million votes had been cast overall with fans, national team captains and coaches, media representatives and a panel of ex-players involved.
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