The 28-year-old forward has received the award for the first time in his career, along with £30,000 to be given to a charity of his choice.
Van Persie's 30-goal haul has matched that of Arsenal legend Thierry Henry in 2003/04, and gives him his third accolade in recent weeks after he took both the PFA and Football Writers' Player of the Year awards.
The Dutchman has been key to the Gunners' success this season, scoring several vital goals which have secured Champions League football for the north London side.
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| 10/1 | The Dutch are 10/1 to open their tournament with a 3-0 win over Denmark with 188BET |
Wayne Rooney finished runner-up to van Persie with 27 league goals, after seeing Manchester United team-mate Dimitar Berbatov pick up the award last year.
Two of Van Persie's strikes have been nominated for Goal of the Season, including a memorable volley against Everton at the Emirates Stadium back in December.