The 68-year-old football manager issued a statement after Arsenal confirmed the news.
He 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.
“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.”
Club owner Stan Kroenke said it was “one of the most difficult days we have ever had in all our years in sport”.
In a statement, he said: “One of the main reasons we got involved with Arsenal was because of what Arsene has brought to the club on and off the pitch. His longevity and consistency over such a sustained period at the highest level of the game will never be matched.
“Arsene has unparalleled class and we will always be grateful to him. Everyone who loves Arsenal and everyone who loves football owes him a debt of gratitude.
“Three Premier League titles, including an entire season unbeaten, seven FA Cup triumphs and 20 successive years in the Champions League is an exceptional record. He has also transformed the identity of our club and of English football with his vision for how the game can be played.”
Mr Kroenke said he had “high ambitions” to build on Wenger’s “remarkable tenure” and wanted to “honour his vision” by making sure Arsenal could compete for the biggest trophies in the sport..
“We must now focus on making a strong finish to the season and ask our millions of fans around the world to join us in paying appropriate tribute to one of the greats of Arsenal’s history and one of the greats of the game,” he added.
Arsenal said they would seek to replace Wenger, who had just one more year left on his contract, as soon as possible.
Despite drawing criticism over performances in recent years, the Frenchman won the league title unbeaten in the 2003/2004 season, earning his team the “invincibles” nickname.