It is the third award won by the Holland international for his prolific form last season, having already landed the PFA players' and writers' awards.
Van Persie scored 37 goals in 48 appearances for Arsenal and is now recognised as one of Europe's top players.
"Robin had an exceptional season and has established himself in the mould of previous top quality Dutch strikers such as Dennis Bergkamp, Ruud Van Nistelrooy and Marco Van Basten," said PFA chief executive Gordon Taylor.
"He's very much in demand and Arsenal fans will be worrying whether Arsenal can get him to stay or whether he will move on to the likes of Manchester City.
"Many of his goals were the best of not just this season, but any season when you think of the quality of some of his volleys.
"He really has been a talisman for Arsenal and as captain has lifted them into qualifying for the Champions League again when all looked lost."
Burnley striker Jay Rodriguez, who signed for Southampton last week, scooped the npower Football League Championship award following his 21 goal-haul last season.
"Burnley born, Jay had some limited experience in their time in the Premier League but has really come good for the club," said Taylor.
Sheffield Wednesday midfielder Jose Semedo won the League One award while Lewis Grabban, the Rotherham United forward, was recognised in League Two.