Arsenal ended their nine-year trophy drought with a dramatic 3-2 extra-time win over Hull City in the FA Cup final earlier this month.
And Wenger, whose previous deal was due to expire in June, has agreed fresh terms that will take him beyond 20 years' service with the Premier League club.
Wenger told the club's official website: "I want to stay and to continue to develop the team and the club. We are entering a very exciting period. We have a strong squad, financial stability and huge support around the world.
"We are all determined to bring more success to this club.
"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, 64, took over at Arsenal in August 1996 and has won three Premier League titles and five FA Cups in his time in London.
The success against Hull at Wembley ended a long wait for silverware, with Wenger's future having been regularly questioned previously due to a lack of trophies.
Arsenal have qualified for the UEFA Champions League in each of the last 17 seasons but have failed to win the league since 2004.
They made the early running in the title race last season but ended up in a battle just to claim fourth spot.
Heavy away defeats against fellow high-flyers Chelsea, Liverpool, Manchester City and Everton put paid to their ambitions, but Wenger has retained the confidence of the club's board of directors.
It remains to be seen whether he will now break the club's tradition of spending relatively modestly in the transfer market, an approach that has been criticised by sections of Arsenal's supporters.
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