The 64-year-old Frenchman, who is the longest serving manager in the Premier League having taken charge in 1996, ended a long wait for a trophy by winning the FA Cup earlier this month.
It was his eighth major trophy with Arsenal, having won the Premier League three times and the FA Cup five times.
A new deal for Wenger had been expected in the wake of the FA Cup success, following a season in which Arsenal appeared ready to challenge for the title before falling off dramatically in the second half of the season as injuries took their toll.
However, Wenger held off the challenge of Everton to qualify for the Champions League for a 17th time.
Former Gunners goalkeeper Bob Wilson, who served as goalkeeper's coach in the early years of Wenger's Arsenal reign, told BBC Radio 5 Live: "This is a guy who works 24 hours a day all year around.
"He hates to lose and revolutionised the game in the country. Some say he has too much power but a guy who dedicates himself to it like he does, you cherish.
"Every club who has built a new ground in this country have all been relegated. Why? Because of the stranglehold of the debt of a new ground. Arsene and Arsenal have got through that stage by still qualifying for the Champions League."
Arsenal later confirmed that Wenger had signed a new three-year extension to his current contract.
He said: "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.
"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."