The long-awaited announcement comes after months of speculation surrounding Wenger's future but the deal will extend the 67-year-old's tenure at the club to 23 years.
And it means Wenger, who has managed 790 Premier League games, is on course to surpass Sir Alex Ferguson's record of 810 matches next season.
Wenger has always had the backing of majority shareholder Stan Kroenke and the pair met on Monday to discuss his future.
There was then a board meeting on Tuesday where Wenger's contract was ratified.
Wenger said: "I love this club and I am looking forward to the future with optimism and excitement. We are looking at what we do well and how we can be stronger everywhere. This is a strong group of players and with some additions we can be even more successful.
"We’re committed to mounting a sustained league challenge and that will be our focus this summer and next season.
Arsene Wenger lifts FA Cup as Arsenal players celebrate Sat, May 27, 2017
Arsene Wenger was the centre of attention during the wild Arsenal celebrations
Play slideshow Getty Images 1 of 11
Arsenal celebrate winning the FA Cup against Chelsea
"I am grateful to have the support of the board and Stan in doing everything we can to win more trophies. It’s what we all want and I know it’s what our fans around the world demand."
Majority owner Stan Kroenke added: “Our ambition is to win the Premier League and other major trophies in Europe. It’s what the fans, players, staff, manager and board expect and we won’t rest until that is achieved. Arsene is the best person to help us make that happen. He has a fantastic track record and has our full backing.”
And chief executive Ivan Gazidis revealed a full review of Arsenal's on and off the pitch activities has been done after finishing fifth in the Premier League.
Gazidis said: "There is no complacency anywhere at this club. Our goal is to compete for and win trophies here and in Europe. Everything we do is designed to make that happen and we will be working hard on and off the pitch this summer to improve and make a strong challenge next season.
"The club has grown beyond recognition in every aspect in recent years and we have the platform to be successful and meet the ambitions we and our fans share."
Get Quotes on Home Insurance
Arsene Wenger has signed a new Arsenal contract
The Frenchman, who won his seventh FA Cup on Saturday, had been reluctant to announce what he intended to do throughout the season.
But he recently admitted the drawn-out affair had an impact on his players as they crashed out of the Champions League to Bayern Munich and finished fifth in the Premier League, the first time they have failed to be in the top four since Wenger became manager in 1996.
The indifferent 2016/17 campaign has seen Arsenal fans call for Wenger to quit using banners, planes and protests.
Does Arsene Wenger deserve to stay?
After winning the FA Cup for a record seventh time, it is understandable that Wenger is reluctant to leave.
But Arsenal have averaged around 73 points in the Premier League over the last three seasons and the last time a team won the title with fewer than 80 was in 1999.
Chelsea won this season's title with 93 with Arsenal 18 points adrift.
Arsene Wenger's 20 best Arsenal signings ranked Wed, May 31, 2017
With Arsene Wenger set to sign a two-year contract extension at Arsenal, Express Sport ranks his 20 best signings
Play slideshow Getty Images 1 of 21
Express Sport ranks Arsene Wenger's 20 best Arsenal signings
In conclusion Arsenal's recent history shows they aren't getting close to winning the Premier League.
And as much as winning the FA Cup is important, the league and Champions League are what fans crave most.
Wenger has been unable to deliver a league title since 2004 and the closest he came in Europe was defeat to Barcelona in the 2006 final.
Did the Arsenal players want Arsene Wenger to stay?
Aaron Ramsey said: "Of course I want him to stay at club. He deserves this.
"We changed the formation and had a lot of success.
"Fair play to him, he changed the system. Hopefully, he'll be there next season."
- Alexis Sanchez and Mesut Ozil to leave Arsenal
- Arsenal pick boss to replace Arsene Wenger once two-year deal is up
Alex Iwobi said in March: "I don’t know exactly what’s going on.
"But me, personally, I’d like him to stay.
"He always backs our players and he is a great man. He’s been great to me as well, I’ll always back him, no matter what."
Can Arsene Wenger convince Mesut Ozil and Alexis Sanchez to stay?
Arsene Wenger's biggest challenge now is to ensure he keeps hold of his star names.
Ozil and Sanchez have led Arsenal a merry dance with their reluctance to sign a new deal and keeping the club on the back foot.
Will Alexis Sanchez and Mesut Ozil be at Arsenal next season?
Fresh reports suggest both players have already made their made up to leave Arsenal due to concerns over the club's ability to compete for major trophies.
But Wenger was able to convince Ozil and Sanchez to join Arsenal from Real Madrid and Barcelona respectively.
Maybe there is a slight glimmer of hope he can get them to stay, because without the world class duo, Arsenal's already tricky looking 2017/18 campaign becomes treacherous.