Wenger has presided over a gruelling season, which saw his team fail to qualify for the Champions League, but masterminded a stunning FA Cup final win over Chelsea last weekend.
The 67-year-old Frenchman's new deal, which will take his tenure up to 23 years, is believed to have been rubber-stamped during a board meeting on Tuesday.
"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," Wenger told Arsenal's website.
Arsenal said Wenger and chief executive Ivan Gazidis had conducted "a full review of our on and off-the-pitch activities" to identify areas for improvement in view of a title challenge.
American majority shareholder Stan Kroenke said: "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."
Arsenal missed out on Champions League qualification for the first time in 20 years and were thrashed 10-2 on aggregate by Bayern Munich in the Champions League last 16.
- 'Absolutely horrendous' -
===========================
Wenger has come under greater pressure from supporters than ever before, with fans holding 'Wenger Out' placards, boycotting home games and chartering planes to trail banners calling for him to go.
The dissent reached a crescendo during a run of seven defeats in 12 games between late January and early April.
But he has been deeply hurt by the criticism he has received, branding the conduct of some supporters a "disgrace" and saying it created a "horrendous atmosphere" around the team.
In an interview on Arsenal's website, Wenger appealed to fans: "Let's be together to support our players, to support the club and all give our absolute best to be at the level that we want to be."
Arsenal's Wembley win against Chelsea gave them a third FA Cup in four seasons and made Wenger the first manager in history to have won the tournament seven times.
His key objectives for the close season will be to tie star duo Alexis Sanchez and Mesut Ozil to new contracts and strengthen his squad for the rigours of a Europa League campaign.
Wenger said Arsenal would only look to sign "top, top quality" players and said having a "very heavy squad" meant "we might lose some players".
"We're committed to mounting a sustained league challenge and that will be our focus this summer and next season," he added.
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