The 24-year-old midfielder becomes the first Algerian to win the award, which is decided by football fans.
Porto winger Brahimi told BBC Sport: “It’s a big honour for me to receive this wonderful trophy. I owe it to my country, Algeria, and to all the people who voted for me.
“It’s also a trophy for the whole of Africa, because it rewards an African player. So I am really very happy.”
After a record number of votes were submitted from fans in 207 Fifa-registered countries, Brahimi came out on top ahead of Nigerian Vincent Enyeama, Gabonese Pierre-Emerick Aubameyang and Ivorian pair Gervinho and Yaya Toure.
And he is thrilled to have been acclaimed as the best player on the continent for the past year.
“This trophy is going to give me more strength, more desire to work, to get better, to learn so that I can keep having great performances,” added Brahimi, who was congratulated in a Tweet by last year’s winner Toure.
During 2014, Brahimi has shone for both club and country.
Brahimi has had an outstanding year and his efforts have been recognised football fans
He starred for Algeria at the World Cup in Brazil, helping them reach the last-16 for the first time and scoring his first international goal in the 4-2 win over South Korea in the group stage.
Domestically, Brahimi started the year at Spanish club Granada, where his strong performances led to him being named best African player in the country last season – and earned him a move to Portuguese giants Porto.
He has scored six goals in 15 appearances for his new club and is revelling in the challenge of European Champions League football, where he hit a hat-trick in the club’s first group match.
“First I won the award because of the people who voted for me. So once again I need to thank them.
“Then it’s thanks for FC Porto – they allowed me to play in the Champions League, to play in big games and to have great performances. The club has allowed me to express myself and to perform well on the pitch.”
Brahimi will also be part of Algeria’s squad to play in the Africa Cup of Nations in Equatorial Guinea from 17 January to 8 February.
“The Africa Cup of Nations is also coming. There are big opportunities for me,” he said. “And I hope I’ll be able to achieve big things this year both with my national team and my club.
“I’m sharing this trophy with my family, with all the African countries and with all the Algerian who have always supported me. Thanks again.”