The 27-year old Senegalese striker was up against his Liverpool teammate Mohamed Salah, the Egyptian who won the award the last two years, and Algerian Riyad Mahrez of Manchester City.
"I am really happy and at the same time I am really proud to win this award," said Mane at the ceremony organised by the Confederation of African Football in the Egyptian Red Sea city of Hurghada.
"It's a big day for me."
Mane became the second star from Senegal to be named African Player of the Year after El Hadji Diouf, who was the continent's best player in 2001 and 2002.
He scored 34 goals and produced 12 assists in 61 appearances in 2019, according to CAF statistics.
Salah's tally stood at 26 goals and 10 assists in 55 matches while Mahrez accounted for 14 goals and 18 assists in 48 games last year.
The key Senegalese player shared the 2018/19 Premier League Golden Boot award with Salah and Arsenal's Pierre-Emerick Aubameyang from Gabon.
"I would love to thank all the Senegalese people. They have been for me all the time, they push me," said Mane, extending sincere gratitude to people from his village Bambali.
- Africa's best in 2019 -
FIFA president Gianni Infantino as well as former Argentinian player Juan Sebastian Veron and Brazil's Cafu attended Tuesday's event.
Some of Africa's former star players including Senegal's Diouf, Egypt's Ahmed Hassan and Algeria's Rabah Madjer were also at the ceremony.
Neither Salah nor Mahrez, who was playing for Manchester City, were present on Tuesday.
Mane, Salah and Mahrez played for their respective countries in the 2019 Africa Cup of Nations.
Salah's Egypt crashed out of the competition shortly after it kicked off but Mane and Mahrez faced off in the final.
Algeria claimed the title following a 1-0 victory over Senegal in Cairo.
At the ceremony, other male awards went to Algerian coach Djamel Belmadi, Algerian Youcef Belaili for African Interclubs Player of the Year and Algeria's national team.
The award for the youth category was given to Morocco's Achraf Hakimi of Borussia Dortmund.
Female awardees included Nigerian Asisat Oshoala, who won the African Women's Player of the Year prize for the fourth time.
South African national team boss Desiree Ellis was also voted top coach for the second consecutive year.
Cameroon's women's team was selected as the continent's best after reaching the last 16 of the World Cup.
The Egyptian Football Association also won the Federation of the Year award.
The CAF Team of the Year featured Salah, Mane and Aubameyang as well as Mahrez and Ajax duo Andre Onana and Hakim Ziyech.
Paris Saint-Germain midfielder Idrissa Gueye was included alongside Senegal team-mate Kalidou Koulibaly, with Hakimi, Joel Matip and Serge Aurier also selected.