Wenger, the Premier League's longest-serving manager, will leave his post at the end of the season.
The decision comes in the wake of last weekend's 2-1 defeat to Newcastle United at St James's Park.
Arsenal are sixth in the Premier League table after another disappointing domestic campaign.
In a statement, 68-year-old Wenger said: "After careful consideration, and following discussions with the club, I feel it is the right time for me to step down at the end of the season.
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“I am grateful for having had the privilege to serve the club for so many memorable years.
“I managed the club with full commitment and integrity. I want to thank the staff, the players, the directors and the fans who make this club so special.
"I urge our fans to stand behind the team to finish on a high. To all the Arsenal lovers take care of the values of the club. My love and support for ever.”