Arsene Wenger has been given a £15m transfer budget and further arrivals are expected this summer, but the Frenchman is delighted with his latest signing.
Wenger said: "Robin is a great young talent and a fantastic signing for the club. He has shown great potential at both club and Under-21 international level and will help strengthen our squad considerably.
"He has a fine left foot and is a great passer of the ball with excellent vision. He is a versatile player and is comfortable playing as a striker or on the wing. We are all looking forward to Robin joining us for pre-season in July."
Van Persie's arrival at Highbury completes a protracted and acrimonious transfer saga that created a certain amount of ill-feeling between the clubs.
Arsenal had a £2.5m bid accepted during the January transfer window but were angered when Feyenoord leaked news of their interest and increased their asking price, forcing them to look elsewhere.
The Dutchman was was shattered when Wenger instead completed the £10.5m signing of Jose Reyes from Sevilla and is delighted to have been given a second chance to join Arsenal. In common with several Wenger signings, such as Reyes and Thierry Henry, van Persie began as a left winger but is equally at home up front.
Van Persie has been a regular in the Feyenoord first team for the past two seasons and helped the club capture the UEFA Cup in 2002, after which he was named 'best young talent' for the season by the Dutch PFA.
His six goals in 27 league appearances this season have helped Feyenoord to third in the Dutch league, with the club close to qualifying for European competition next season.
