Gazidis is tasked with bringing in a new boss for the start of 2018-19 following Wenger's announcement that this season will be his last in charge.
The Frenchman has won three Premier League titles and a record seven FA Cups during his time in North London, but the club are on course for their worst-ever finish in the Prem era as they are struggling in sixth place.
Speaking at a press conference on Friday evening, however, Gazidis claimed that Arsenal are in good hands and well positioned to make an appointment.
"He leaves us in a very strong position to look forward," he told reporters. "Arsene earned his position at this club over 22 years. I don't think there will be other managers who will have that authority at the top of the game at the biggest clubs. It's the most important appointment any club makes and still the most important employee any club has.
"It would be unrealistic to think anyone comes in with the breadth and scope Arsene has at Arsenal Football Club. Arsene changed the game, set a totally new standard, a new ambition, not just to win but to win while achieving perfection - to make art out of football. He was always brave enough to be true to that ambition and achieved it with the Invincibles.
"Arsenal truly has a football philosophy and he has been brave enough to live by it - reinvented the game and played some of the best football we've ever seen. The decision had to happen at some point. I don't think the club has ever been better prepared for that decision. Now it's time to look forward, and I think we can do that with confidence."