Arsenal chief executive Gazidis said at the formal confirmation of the kit deal: "We are excited to be partnering with Puma, a company whose football heritage and record of innovation have a strong affinity with our own. This represents another important step forward in Arsenal's progression on and off the pitch."
When asked about the contract status of his manager, Gazidis gave Arsenal fans the news they wanted to hear and said: "Arsene will be extending with us and at the right time we will make that announcement."
Though Arsenal have not won a trophy in eight years, their form this season and the inspired capture of Mesut Ozil has led to renewed hope that another era of success under Wenger is forthcoming.
Puma is ousting US group Nike which has provided Arsenal's red and white shirts for the past two decades.
The agreement shows Puma's determination to re-establish itself as a core sports brand under new CEO Bjoern Gulden after moving more into lifestyle and fashion.
Puma has also acquired the rights to produce other branded Arsenal merchandise that will be sold to fans around the world.
Financial details were not disclosed but Puma said the deal was the biggest ever for both itself and Arsenal.
In 2012, Arsenal signed a contract renewal with airlines Emirates for shirt and stadium sponsorship worth £150m over five years.
Puma, which supplies kit to German club Borussia Dortmund and national teams including Italy, said it was aiming to establish itself as the clear number-three football brand.
Adidas and Nike dominate a global market worth an estimated 4.5 billion euros per year, and US brands such as Under Armour and Warrior have also been expanding in the sport.
"Arsenal represents a major commercial and marketing opportunity to reinforce Puma's credibility as a global sports brand," Gulden said in a statement.
The Puma deal is no surprise after news of it leaked on social media late last year. However, Arsenal fans are likely to press the club to spend heavily before the player transfer window closes at the end of the month to boost the team's push for a first trophy since 2005.
The Nike deal was worth £38m for United in 2012-13, including the club's share of profits from merchandise sales. United and Nike are in negotiations on a new deal.