The Frenchman departs a year before his latest contract was due to expire.
The Gunners are sixth in the league and set to miss out on a top-four spot for the second straight season, with their hopes of reaching the Champions League resting on winning the Europa League.
Wenger, 68, won three Premier League titles and seven FA Cups, including the Double in 1998 and 2002.
"I am grateful for having had the privilege to serve the club for so many memorable years," said Wenger. "I managed the club with full commitment and integrity.
