Senegal forward beat Liverpool team-mate and Egypt forward Mohamed Salah and Manchester City’s Algerian winger Riyad Mahrez to the award.
Mane, 27, helped the Reds to the 2018-19 Champions League title, scoring 30 goals in all competitions last season.
He has scored 15 goals so far in 2019-20, with Liverpool 13 points clear at the top of the Premier League table.
“I’m really happy and proud to win this. Football is my job, I love it,” said Mane.
“I would like to thank my family, my national team, staff, the federation, and Liverpool Football Club. It’s a big day for me.”
Mane collected his award at a ceremony in Hurghada, Egypt but neither Salah, who had won the award in both the past two years nor Mahrez were present.
Mane has finished in the award’s top three for the last three years and has long targeted the prize in order to emulate the achievement of one of his heroes, former Liverpool striker El Hadji Diouf, who won it in 2002.
Nigeria and Barcelona forward Asisat Oshoala was named the African Women’s Player of the Year ahead of Valerenga and Cameroon forward Ajara Nchout and Beijing BG Phoenix and South Africa forward Thembi Kgatlana.
Cameroon, who lost 3-0 to England in the last 16 of the 2019 Women’s World Cup, picked up the prize for African Women’s National Team of the Year, with Africa Cup of Nations winners Algeria taking the men’s honour.
Djamel Belmadi, who guided Algeria to the Afcon title, won Men’s Coach of the Year, with Diseree Ellis, the coach of the South Africa national team, winning the women’s award.