The new deal which will be announced on Wednesday, follows a board meeting with the Frenchman on Tuesday afternoon.
The uncertainty over Wenger’s future may have affected the Gunners this season, after the team finished fifth in the Premier League, their worst finish for 21 years.
Wenger conceded that they had played in an “absolutely horrendous” psychological environment.
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However, the North London side produced one of their best performances to beat Chelsea 2-1 and win a record 13 FA Cup titles.
With Wenger’s contract now settled, the Frenchman faces a growing list of problems to solve next season, which includes spending big and keeping hold of their key players, Alexis Sanchez and Mesut Ozil, who are both out of contract at the end of next season.
Wenger joined Arsenal on 22 September, 1996, replacing Bruce Rioch, to become the clubs most successful manager.