Danish striker Bendtner was in his final year of his current contract.
“It means a lot that I can commit my future to Arsenal because I have a great affection for this club,” Bendtner told the club’s official website.
“I’ve been here for five years now, and my development both on and off the pitch as a player and person is thanks to Arsene Wenger and the team here.
“We’ve got a group of players that is capable of achieving great success, and I am really excited to be a part of it.”