Van Persie has been in impressive form this season and is the Barclays Premier League's leading goalscorer with 27 goals. He has scored 34 goals in all competitions.
FWA chairman Steve Bates, chief football writer at The 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."
Van Persie, who joined Arsenal in 2004, will receive the FWA award at a gala dinner in London on 3rd May.
It is the second time in three days that Van Persie has been honoured, after he received the Professional Footballers' Association's Player of the Year award on Sunday.
Rooney has also been in prolific form this season, scoring 26 times to
help his side move to the top of the League table with only three matches to go.
Scholes, regarded as one of the finest midfielders of his generation, finished in third after showing tremendous form since coming out of retirement in January.
United States international Dempsey, meanwhile, has scored 16 goals in 34 appearances for Fulham with many of his goals being scored when deployed in midfield.