The Egyptian pipped Manchester City star Kevin de Bruyne to the prize by just 20 votes in a ballot of over 400 FWA members that saw Tottenham Hotspur striker Harry Kane finish third.
Salah becomes the first African ever to win the award, and will be presented with the trophy at an event in London on May 10.
Late last month, the 25-year-old was named the Professional Footballers' Association's Player of the Year after winning a poll of his peers.
The two prestigious gongs come as recognition for a remarkable first campaign at Anfield that has seen Salah net 43 goals in just 48 appearances in all competitions.
The Reds forward joins Ian Callaghan, Kevin Keegan, Emlyn Hughes, Kenny Dalglish (twice), Terry McDermott, Ian Rush, John Barnes (twice), Steve Nicol, Steven Gerrard and Luis Suarez in winning the award while representing Liverpool.