The 65-year-old's current deal is due to expire this summer, but the club is set to wrap up negotiations with the Frenchman regarding new terms, with a huge cash injection from a club-record new kit deal set to give Wenger even greater spending power.
"We've always supported Arsene. The board has always been completely behind him, and Arsene has always been committed to this football club," Gazidis said. "We are comfortable in our position, we're relaxed about it, and Arsene will be extending with us. At the right time we will make that announcement."
Gazidis was speaking at the unveiling of the Gunners' new club-record kit manufacturing contract with Puma, which will allow Arsenal to commit further cash to Wenger's transfer pot as soon as the deal takes effect July 1.
"One of our long-term goals has been to increase our commercial revenues and there's a football reason for that as we want to invest that in our squad," Gazidis said. "So this is a very important step in terms of our progression on the pitch, and from this summer onwards the money will be available to the manager to use in the way that he thinks best."
Arsenal has been steadfast in its stance against inflated spending in the game, and the CEO believes that the Puma deal gives more power to the club in its continued fight for greater ethics.
"I think it is a validation of the things we are doing right. We are in a challenging environment, as you see from the escalation in transfer fees and player salaries. Our club has walked an independent path, standing on our own two feet, and thinking long term about that progression.
"We are delighted to be partnering with an organization that saw the vision of what we are doing and believed in it, and we believe this is going to be very exciting for us to be able to work together. I think we are stronger together as we look forward, and we as a football club are moving forward not just off the pitch but more importantly on the pitch."
Gazidis hopes that the agreement with Puma will alleviate the financial burden on supporters without curtailing the club's plans to back Wenger's vision in the transfer market, while he also see's UEFA's Financial Fair Play rules as another key in reducing costs for the everyday fan.
"We've been explicit in saying as a club that we've been very dependent on our ticket prices through the move to the new stadium, and it's important for us to diversify our revenue streams and expand. Broadcasting revenue expands on its own, we don't control that, but it's important to expand our commercial revenue base. This deal does that and helps us take a further step down that road.
"More globally for football, what we hope to see moving forward is more responsible spending in the game. I think if that happens it will produce a more rational environment, and that begins to take more pressure off ticket pricing. So we're looking forward to UEFA's Financial Fair Play.
"We remain healthy sceptics about that but I had lunch with Michel Platini this week and he continues to assure everybody who's concerned about this in the game that we will see positive inforcement from UEFA. I think if that happens then we'll see it take a little of the edge off the spiral that we see in spending."