Arsenal chief executive Ivan Gazidis admitted it had been "an emotional day" and explained that Wenger was busy preparing for Sunday's game against West Ham.
In a pres conference held this aftenoon, following Wenger's announcement he was going to step down, Gazidis faced questions from the press.
"His focus is on the game - that's who he is," he said.
Gazidis added: "He has transformed the beautiful game and made Arsenal famous throughout the world for the style of football we play.
"He is able to make people believe they can achieve great things, on and beyond the football pitch.
"The foundations of this club have never been stronger."
"Our first priority is to come together as a club. Look at the outpouring of affection from the Arsenal family and the football family," Gazidis said.
"We will give him the send-off he deserves.
"I have often said (replacing Wenger) is the biggest challenge we face. In the coming months the world will see the unity and power of this football club, and the people within it."
Asked how difficult it would be to replace him, Gazidis said: "We're not going to find a replacement for Arsene Wenger.
"He is an extraordinary man. It is unthinkable to me that we will have another manager - at Arsenal or elsewhere in the Premier League - who stays in their post for 22 years."
Gazidis was asked whether the Frenchman would have a hand in identifying his successor, and replied: "We are going to have a process, that begins today. But I want that to be in-house. We will go through a respectful process. Out of respect for this man we haven't had any discussions to date."
Regarding the timing of the announcement, with five league games and the Europa League final stages still to come, Gazidis said: "We wanted the opportunity that the Arsenal family could come together and I think we are going to see some fantastic atmospheres from now until the end of the season.
"And also, both Arsene and the club needed time to prepare - we have a condensed summer with the World Cup, with a shortened transfer window.
"The reaction today at the training ground, we saw an incredible amount of passion, the players coming together with a desire to give Arsene the send-off he deserves.
"The decision had to happen at some point. I don't think the club has ever been better prepared for that decision. Now it is time to look forward and I think we can do that with confidence."
Gazidis continued: "For me personally, it's been 10 years and it's not just a working relationship, it's a personal relationship. We've been through a lot together and for me it's a highly emotional day.
"Speaking with members of staff you get the sense of just how impactful today is. It feels very, very big. We're still assimilating that but tomorrow we have to start looking forward.
"We're going to take what Arsene has given us and take that forward. I will make sure we do that."