The 68-year-old Frenchman has been at the north London club since 1996.
He is the longest serving manager still in the English Premier League, but has been under pressure in recent years from a disgruntled section of fans.
"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," Wenger wrote in a statement on the Arsenal website.
"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."
Currently sixth in the Premier League, Arsenal is 14 points off fourth place -- the top-flight's last Champions League qualification slot -- but faces Atletico Madrid in the Europa League semifinals next week.
Victory in that competition would qualify Arsenal for next season's Champions League.
"I urge our fans to stand behind the team to finish on a high," added Wenger. "To all the Arsenal lovers take care of the values of the club. My love and support for ever.
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