The deal will see Wenger extend his reign at the Gunners to 23 years.
The Frenchman came under fire following Arsenal's failure to finish in the top four this season for the first time since he joined the club in 1996.
However, the Londoners won the FA Cup on the weekend for a record 13th time by beating English champions Chelsea 2-1 in the final at Wembley.
Wenger subsequently met with club owner Stan Kroenke this week where the terms of an extension were thrashed out.
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.
“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.”