The 25-year-old, who has scored 17 Premier League goals this season, helped Egypt reach the World Cup and Africa Cup of Nations final in 2017.
He finished ahead of Liverpool team-mate and Senegal winger Sadio Mane.
Mane and Salah attended the ceremony in Ghana’s capital Accra, 24 hours before Friday’s FA Cup game against Everton, the latter ruled out with injury.
Borussia Dortmund and Gabon striker Pierre-Emerick Aubameyang came third.
"Winning this award is a dream come true, 2017 was an unbelievable year for me," Salah said after receiving the trophy.
"I would like to dedicate it to all the kids in Africa and Egypt, I want to tell them to never stop dreaming, never stop believing."
Salah, who was voted the BBC African Footballer of the Year in December, has enjoyed a stellar year for both club and country.
In early 2017, the forward was the central figure for Egypt as they finished runners-up at the Africa Cup of Nations.
He also had a hand in all seven of the goals that took the Pharaohs to their first World Cup since 1990 - assisting two and scoring five, including the stoppage-time penalty against Congo that saw them qualify them for Russia.
Salah’s form at club level has been every bit as impressive as it has in internationals.
In Italy, he scored 15 goals and made 11 others as he helped Roma finish second in Serie A, before joining Liverpool, where he has scored 23 goals in 29 games so far for Jurgen Klopp’s side this season.
Speaking about his Liverpool team-mate Mane, Salah suggested the Senegalese is on course to win the Player of the Year award himself in the future.
"I am very happy and very proud to share this moment with my friend, and I am sure he is going to win it very soon," he said.
The Women’s Player of the Year award was won yet again by the former Liverpool and Arsenal star, Asisat Oshoala of Nigeria, who now plays for Dalian Quanjian in China.
She faced some criticism for her move, but said her success in winning the title for the third time proved she made the right decision.