Wenger’s new two-year contract at the Emirates was announced on Wednesday.
The announcement brings to an end months of uncertainty, after a turbulent campaign.
For the first time in his 21 years at the club, Wenger failed to guide the Gunners into the Premier League’s top four, missing out on the Champions League despite winning nine of their last 10 games.
However, Gazidis insists that Wenger remains the best man for the job at the Emirates.
“When you look at the world of football, and you think about the great candidates that there are – and there are many great coaching candidates in the world and Arsenal is a club that all of them would want to work for because of the things we represent in football,” said Gazidis.
“But when you look around and make that assessment, you don’t find any better candidates than Arsene Wenger.
“I think in football, the judgements are so black and white that often, if you don’t fire your manager, then you’re seen as being unambitious,” he added. “I think that’s ludicrous.
“You don’t fire good people, you don’t fire people who are world-class, you don’t fire people who are driven to improve.
“What you do is work out how you can improve together and how you can move forward. That’s what this club is doing and we have a very clear ambition that we want to deliver it in.”
Wenger has split Arsenal fans and some sections of the support have greeted the news that the 67-year-old remains in power with dismay.
But Gazidis has called on the club’s supporters to get behind the Frenchman, now that the uncertainty has been put to an end.
“I’m convinced that our fanbase will put the football club at the top of their priorities and will get behind this team,” he said.
“Together, we are much, much stronger than we are when we are arguing and trying to prove who’s right and who’s wrong. Let’s get behind the team, let’s get behind the club.”