Mane beat team-mate and Egypt forward Mohamed Salah and Manchester City’s Algerian captain 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 so far scored 15 goals this year, with Liverpool 13 points clear at the top of the Premier League table.
He told BBC that: “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,” he added.
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.
This time he broke the jinx after three unsuccessful bids having featured among the finalists for the last three years. He becomes only the second Senegalese to win the award, after former Liverpool striker El Hadji Diouf, who won it in 2002.