The Dane will leave Arsene Wenger's side at the end of the month, while South Korea forward Park Chu-Young has also been released
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The 26-year-old forward joined Arsenal in 2004 and has made 171 appearances for Arsene Wenger's side in all competitons.
Bendtner, who had been loaned out to Birmingham City, Sunderland and Juventus during his time at Arsenal, featured just nine times in the Premier League last season.
Also among those leaving the club is Bacary Sagna, who has agreed a deal to join Manchester City. Lukasz Fabianski will move to Swansea City, while 20-year-old forward Zak Ansah is joining Charlton Athletic.
Park Chu-Young, who is currently at the World Cup with South Korea, has also been released by Arsenal.
Kim Kallstrom is returning to Sparktak Moscow after arriving in January on a six-month loan. The Sweden international made just four appearances last season having arrived at the club with a back injury.
Italian goalkeeper Emiliano Viviano returns to Palermo following his season-long loan spell.
Meanwhile, academy players Chuks Aneke, Daniel Boateng, Zach Fagan and Leander Siemann have not been retained.