Al-Dawsari, who scored Saudi Arabia's winner in their shock 2-1 victory over Argentina at the World Cup last year, took the men's award after also leading Al Hilal to the final of the Asian Champions League and the Club World Cup.
The awards were being held for the first time in four years as a result of the disruption caused to the game across the continent by the COVID-19 pandemic.
"I am very happy with this achievement and I would like to thank the leadership in Saudi Arabia for their keen interest in athletes and support for sport," said Al-Dawsari, who won ahead of Qatar's Almoez Ali (27) and Mathew Leckie (32) of Australia.
Kerr, who on Monday had finished as runner-up in the Ballon d'Or vote in Paris, won her award for the second time having previously been named the confederation's best female player in 2017.
She becomes the third woman to claim the award more than once, joining Japanese duo Aya Miyama (38) and Homare Sawa (45) as a multiple title-holder.
"I just want to say what an amazing honour it is to win this award, especially up against some amazing finalists," said Kerr, who was given the award ahead of China's Zhang Linyang (22) and Saki Kumagai (33) from Japan, the 2019 winner.
Japan's Hajime Moriyasu (55) won the trophy for best men's coach after leading the Samurai Blue to the last 16 at the World Cup, with victories over Germany and Spain in the group stage of the tournament.
Shui Qingxia (56) claimed the honours in the women's coaching category after she led China to the Women's Asian Cup last February in India, the country's first continental title since 2006.
