The Gunners captain cemented the top spot by an "overwhelming" number of votes by journalists around the country, with Manchester United frontman Wayne Rooney claiming second place, Paul Scholes snatching third and Fulham forward Clint Dempsey coming in at fourth spot on the list.
Dutch international Van Persie, who has scored 34 goals in all competitions for Arsenal this season, was the clear favourite from the off.
Football Writers' Association chairman and chief football writer at The People Steve Bates 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."
The 28-year-old will pick up the award during a gala dinner at the Lancaster London Hotel on May 3.