The 25-year-old beat 2015 winner Patrick-Emerick Aubameyang of Gabon and Senegal striker Sadio Mane. He received his award at Thursday's ceremony in Abuja, Nigeria.
Mahrez was a key player as English underdog Leicester City won the Premier League title for the first time in its history in 2015-16, defying 5,000-1 odds.
The Foxes have struggled to repeat that success domestically this season, but Mahrez has helped the team reach the last 16 of the Champions League in its debut appearance in Europe's top club competition.
He is the first north African to win the award since Morocco's Mustapha Hadji in 1998.
Two Algerians won the prize when it was run by France Football magazine -- from 1970-94, with joint awards in the latter three overlapping years. Rabah Madjer triumphed in 1987, and Lakhdar Belloumi did so six years earlier.
African Player of the Year - Based in Africa
Since its inception in 1992, all winners of the CAF African Player of the Year have been playing in Europe.
In 2005, a separate award for Africa-based talent was started -- and this year's winner is Ugandan Denis Onyango, who plays for South African club Mamelodi Sundowns.
Other award winners
CAF African Women's Player of the Year: Asisat Oshoala (Nigeria & Arsenal Ladies)
CAF African Coach of the Year: Pitso Mosimane (Mamelodi Sundowns)
CAF National Team of the Year: Uganda
CAF Most Promising Talent of the Year: Kelechi Iheanacho (Nigeria & Manchester City)
CAF Youth Player of the Year: Alex Iwobi (Nigeria & Arsenal)