Van Persie, 28, has been the Gunners' standout player in recent years and, at times, carried the side last season, scoring 30 Premier League goals.
In an open letter to fans on his website, www.robinvanpersie.com, he wrote: "I've thought long and hard about it, but I have decided not to extend my contract."
Van Persie confirmed he had met with Arsene Wenger, the Arsenal manager, and the chief executive Ivan Gazidis at the end of last season to discuss his future but, in a worrying development for fans of the club, indicated he did not receive the answers he was looking for. The Dutchman, who signed for the London club in 2004 from Feyenoord, has won just one major trophy with Arsenal, the FA Cup in 2005.
He cited a desire for silverware as his primary motive for deciding to leave the Emirates.
Van Persie wrote: "This is an update for the fans about my current situation. 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.
"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 should move forward."
Van Persie appeared to predict an adverse reaction from the club's supporters but went out of his way to offer conciliatory words about his time in north London - notably choosing to directly address supporters.
"You guys, the fans, have of course the right to disagree with my view and decision and I will always respect your opinions," he wrote.
"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."
Arsenal will now be expected to invite offers for their prize asset, but there have been suggestions they may choose to hold on to him next term and let him go on a free transfer. The size of any potential offers could determine their decision.
Arsenal issued the a statement after later in the day: "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."
As for his next move, Van Persie said: "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."
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