The 25-year-old joined the Gunners from Feyenoord in 2004 and was Arsenal's leading scorer last season with 20 goals from 44 appearances in all competitions.
The club have not made the length of the new deal public, but manager Arsene Wenger told Arsenal's website: "It's fantastic news that Robin van Persie has committed his long-term future to Arsenal Football Club, we're all delighted.
"At only 25, there is still much more to come from him. Robin has the potential to become a true Arsenal great."
Van Persie added: "We have a top class manager, a squad full of superb young players, a world class stadium and brilliant supporters. Arsenal Football Club has a very bright future and I want to be part of it."
In his five seasons with Arsenal, Van Persie has made 177 appearances and scored 63 goals in all competitions.
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