The agreement does not include a break clause and, should it be completed, will extend his reign to 23 years.
Neither Arsenal nor Wenger, 67, see this as definitely being his final contract.
Arsenal are expected to spend at least £100m on new players in the upcoming transfer window - which opens on 1 July - having also spent around that figure last summer.
The Gunners finished fifth in the Premier League this season, the first time they have finished outside the top four since the Frenchman joined in 1996.
They finished 18 points behind champions Chelsea, but beat the Blues 2-1 to win the FA Cup at Wembley on Saturday.
Wenger met club owner Stan Kroenke on Monday to determine his future, with the decision relayed to directors at a Tuesday board meeting.
An official announcement is expected later on Wednesday.
Analysis
Although Arsenal may have £100m to spend, the issue is that they already have a high wage bill and their revenues are not as large as Europe's very biggest clubs. And that's before you factor in dropping down from the Champions League to the Europa League.
They need to be careful when it comes to Financial Fair Play, meaning they will inevitably have to sell some players to free up funds for wages rather than transfer fees. It will be a busy few months at the Emirates.
A reign of two halves
Wenger led the Gunners to three Premier League titles and four FA Cups in his first nine seasons in charge.
In 2003-04, he became the first manager since 1888-89 to lead a team through an entire top-flight season unbeaten.
But after winning the 2005 FA Cup, they had to wait another nine years - or 3,283 days - for their next silverware. It came as they beat Hull City to win the 2014 FA Cup, before winning the trophy again the following year.
Arsenal are have not won the Premier League in 13 years and in 11 of those seasons have finished 10 or more points adrift of the champions.
Arsenal have not qualified for the Champions League for the first time in 20 years - and many would believe an FA Cup triumph would be the perfect parting point, allowing Wenger to go out on a high and a successor to usher in the new era.
Wenger does not think in those terms. He is the eternal optimist who has never felt Arsenal were far away from recreating a title-winning team, even though the evidence against has piled up before him.
A section of Arsenal's support have organised protest marches and made their discontent clear as Wenger's side once again failed to halt a barren title sequence stretching back to "The Invincibles" season of 2003/04 - with the manager describing some of his treatment as "a disgrace".
However, he is committed as ever, even after 1,175 games as Arsenal manager, 676 wins and a remarkable win percentage of 57.5% - but did Saturday start a new era of success that can emulate his early glories, or will he simply face the same criticism again at the first sign of trouble next season?
Arsenal are further behind than Wenger thinks'
Match of the Day presenter and former England striker Gary Lineker:
Arsenal have got a long way to go at the moment. If you ask me now whether they are going to be in the top four next season, I would say most probably not. They are further behind than Wenger thinks.
The only other example of a manager that decides when and where he goes is Sir Alex Ferguson, but he was still winning league titles. Arsene Wenger was still winning FA Cups and until this season he had always got in the top four, but now that's changed.
Former Arsenal goalkeeper Bob Wilson:
Without the Champions League, the only way is if you can compete salary-wise to attract the players. Chelsea bought the best player available last season in N'Golo Kante and Arsenal went for him too but came nowhere near the salary that Chelsea pay.
Arsenal cannot compete with Manchester United, or Chelsea with all the money Roman Abramovich has, or Sheikh Mansour has at Manchester City - these are clubs who can manage to go into huge debt.
Wenger staying means...
We asked you on Sportsday to complete the sentence above:
Ally McIntosh: "He's purely in it to try and pass Sir Alex Ferguson's 26 years. Not to win things."
Si Hawkes: "We'll be having this same conversation in two years after he's signed yet another two-year deal."
James Tall: "Another two years of inconsistency and fan frustration."
Alex Maple: "More work for pilots of small planes and banner makers."
We also asked you on Tuesday to vote on whether Wenger staying is a good thing for Arsenal. There were more than 250,000 votes - 58% said yes and 42% said no.
