Tuesday's announcement came just a few days after the Dutch international won the equivalent Professional Footballers' Association (PFA) award and meant the 28-year-old had collected English football's two most prestigious individual honours in the same season.
Van Persie topped the poll of journalists with an overwhelming victory ahead of Manchester United forward Wayne Rooney in second place and his Old Trafford team-mate Paul Scholes third, and Fulham's Clint Dempsey fourth.
The Gunners forward has scored 27 Premier League goals so far this season - his best return for Arsenal.
Van Persie will receive the FWA accolade, which has been running since 1948, at a gala dinner in London on 3 May.
FWA chairman Steve Bates, chief football writer at The Sunday People, said: "Robin was the overwhelming choice of our members this season and deservedly so after a magnificent campaign for Arsenal.
"The quality of his goals, attacking movement and consistency in a turbulent season for The Gunners has been eye-catching. The considerable size of his majority in the votes cast by our members reflected the general view that he has been the season's most outstanding individual performer."