The 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.
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