The Egyptian becomes the first African to be given the accolade after edging out Manchester City midfielder Kevin De Bruyne by less than 20 votes in a ballot of more than 400 FWA members.
Tottenham striker Harry Kane came third, with Salah and De Bruyne polling over 90% of the votes.
Salah is on course to win the Premier League Golden Boot with 31 goals in 34 games and has helped Liverpool to the Champions League semi-finals with 11 goals in 13 matches.
He is the sixth player in seven seasons to complete the awards double, having also been named player of the year by the Professional Footballers’ Association this month.
The 25-year-old, a £39.5m summer signing from Roma, is just the third Liverpool player to win the FWA award in the Premier League era, after Steven Gerrard in 2009 and Luis Suarez in 2014.
FWA chairman Patrick Barclay told Sky Sports News: “You judge a victory against the opposition and in particular from Kevin De Bruyne this season, it has been as good as it gets.
“He [De Bruyne] could easily have won it. It was a very close vote.
“[Salah] has been relentless because you expect a player of his quality to have spells and then quiet spells.
“Whenever you think he can’t do anymore he scores two world class goals against Roma. He has just been phenomenal.
“He makes time stand still – he has that quality which only the Lionel Messis, the greatest players have.
“He has become world class in a year, along with the year he had at Roma. He has shot up to such a high standard.
“There have been comparisons with Lionel Messi after his recent performances and they are not exaggerated.”
Other players to receive votes from FWA members were: Sergio Aguero, Christian Eriksen, Roberto Firmino, Nick Pope, David Silva, Raheem Sterling and Jan Vertonghen.