As revealed by Goal, the Frenchman agreed an extension in principle in October but, since that time, a two-year deal has become three after the Gunners returned to winning ways with triumph in the FA Cup final.
"I want to stay and to continue to develop the team and the club. We are entering a very exciting period," he told the club's official website.
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"The club has always shown faith in me and I'm very grateful for that. We have gone through fantastic periods and also periods where we have had to stick together.
"Every time when that togetherness was tested I got the right response. I think I have shown some loyalty as well towards this club and hopefully we can make some more history. I am sure we can.”
Wenger turned down a £1 million-per-year pay rise in March in agreeing the broad strokes of the deal.
And, despite the contract remaining unsigned as the season drew to a close, the Frenchman began earnest discussions with chief executive Ivan Gazidis in April about the club's transfer plans for the summer.
Still, Wenger harboured a private determination to see what Arsenal could achieve before the season closed, with a top-four finish and FA Cup victory thought to be key to his eventual decision on a new deal.
Arsenal have long been confident of their legendary boss, who passed 1000 games in charge of the team this season, prolonging his spell at the Emirates Stadium, with director Lord Harris claiming in May that Wenger was "always staying".
The Gunners did go on to finish fourth in the Premier League this season, guaranteeing a 17th consecutive year of Champions League football for the club.