Speculation has been rife over the future of the forward, who is entering the final year of his contract.
Arsenal manager Arsene Wenger stated the importance of keeping Van Persie at the club earlier this month but the 28-year-old Dutchman has decided against prolonging his deal.
Van Persie told his official website: "I've thought long and hard about it, but I have decided not to extend my contract.
"You guys, the fans, have of course the right to disagree with my view and decision and I will always respect your opinions."The striker had previously kept quiet over his future and refused to commit to a decision until Wednesday.
Van Persie says he has chosen not to extend his deal following talks with Wenger and chief executive Ivan Gazidis over the club's plans for the future.
He added: "I have kept quiet all this time out of respect and loyalty for the club and as agreed with Mr Gazidis and Mr Wenger, but since there is so much speculation in the media, I think it is fair for you guys to know what's really going on at the moment.
"As announced earlier this year I had a meeting with the boss and Mr Gazidis after the season. This was a meeting about the club's future.strategy and their policy. Financial terms or a contract have not been discussed, since that is not my priority at all.
"I personally have had a great season but my goal has been to win trophies with the team and to bring the club back to its glory days.
Watch: RVP set to leave Gunners.. More Videos
"Out of my huge respect for Mr Wenger, the players and the fans I don't want to go into any details, but unfortunately in this meeting it has again become clear to me that we in many aspects disagree on the way Arsenal FC should move forward."
Van Persie, who joined Arsenal from Feyenoord in 2004, added: "I love the club and the fans, no matter what happens. I have grown up and became a man during my time with Arsenal FC.
"Everybody at the club and the fans have always supported me over the years and I have always given my all (and more) on and off the pitch. I am very proud of being part of this fantastic club for the last eight years.
"As soon as Mr Gazidis is back from his two-week holiday in America further meetings will follow and I will update you if and when there are more developments."
Van Persie ended last season as the Premier League's top scorer with 30 goals, helping the Gunners to a third-placed finish.
Reigning Premier League champions Manchester City have been linked with a move for the prolific forward, while European heavyweights Barcelona, Real Madrid and Juventus are all thought to be interested.
The Gunners won't want to lose their star striker but could sell to avoid losing him on a free transfer when his contract expires next summer.
Arsenal later issued a short statement on their official website which read: "We have to respect Robin's decision not to renew his contract.
"Robin has one year to run on his current contract and we are confident that he will fulfil his commitments to the club.
"We are planning with ambition and confidence for next season with Arsenal's best interests in mind."