The Holland striker, 28, topped the Football Writers' Association poll with a landslide victory ahead of Manchester United forward Wayne Rooney in second place and his Old Trafford team-mate Paul Scholes third, with Fulham's Clint Dempsey fourth.
"It makes me very proud to be here, I have seen the list [of previous winners], and for me, I never really thought I would be sitting here winning this trophy," Van Persie said.
"But even this season I was not really thinking about winning a trophy for myself, I was just playing because I love it and for Arsenal to finish as high as possible in the league.
"When I found out I had actually won it, I was a bit surprised, and was like 'what me? Really?'
"It makes me really proud to be part of that history."
Van Persie, who has yet to agree a new, long-term deal with the Gunners, revealed being honoured by both his peers and journalists alike was a humbling experience.
The Dutchman added: "The writers know everything about the season because they have seen every single game, analysed ever goal, every move, they know everything about you.
"They are doing interviews with me and other players, they get a clear picture of who is the best player, which is why it means so much that these guys have voted for me."