Wenger, 68, will leave a year before his existing contract was due to expire having led the club to three Premier League titles and seven FA Cups during a 22-year reign, Sky Sports reported.
Appointed on October 1, 1996, the Frenchman is the Premier League's current longest-serving manager and has taken charge of a record 823 games.
In a statement to the club's website, 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 forever."
Wenger himself said on Thursday that former Arsenal midfielder Patrick Vieira "has the potential" to succeed him as manager.
The club's majority owner Stan Kroenke asked Arsenal fans around the world to pay an appropriate tribute to the Frenchman who transformed the identity of the club.
He told Arsenal's website, "This is one of the most difficult days we have ever had in all our years in sport. One of the main reasons we got involved with Arsenal was because of what Arsène 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.
"Arsène 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.
"We have high ambitions to build on Arsène's remarkable tenure and to honor his vision by ensuring that Arsenal competes for and wins the biggest and most important prizes in the game.
"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."
Sunday's 2-1 defeat to Newcastle was Arsenal’s 11th in the league this season, equaling their worst tally in a campaign under Wenger.
Arsenal finished outside the league's top four last season for the first time since Wenger arrived at the club in 1996, and is now 14 points behind fourth-placed Tottenham, with five matches remaining.
The Gunners face Atletico Madrid in the Europa League semifinal with the first leg to come on April 26.