Vinicius was beaten to the coveted Ballon d'Or title by Rodri, but has won FIFA's official award after leading Real Madrid to domestic and Champions League titles last season.
Bonmati, meanwhile, helped her club to a domestic treble last season - a campaign in which Barça also retained the Champions League.
Bonmati also scored in the semi-final and final as Spain won the UEFA Nations League in February.
Men's awards
Player of the year: Vinicius Jr
Coach of the year: Carlo Ancelotti
Goalkeeper of the year: Emiliano Martinez
XI of the year: Emiliano Martinez, Dani Carvajal, Ruben Dias, William Saliba, Antonio Rüdiger, Rodri, Toni Kroos, Jude Bellingham, Lamine Yamal, Erling Haaland and Vinicius Junior
Women's awards
Player of the year: Aitana Bonmati
Coach of the year: Emma Hayes
Goalkeeper of the year: Alyssa Naeher
XI of the year: Alyssa Naeher, Lucy Bronze, Irene Paredes, Naomi Girma, Ona Batlle, Aitana Bonmati, Lindsey Horan, Gabi Portilho, Patri Guijarro, Caroline Graham Hansen, Salma Paralluelo