The deal will run from 1 July 2014, but the club have not revealed details of how much they will receive or for how long the deal will run.
Arsenal CEO Ivan Gazidis was delighted with the news.
"We are excited to be partnering with PUMA. It represents another important step forward in Arsenal's progression on and off the pitch," he told the club's official website.
The deal with Puma ends Arsenal's long association with Nike, who have manufactured the club's official kit for the last 20 years.
Bjoern Gulden, chief executive officer for PUMA said: "Arsenal have been a key strategic target for PUMA for a number of years now.
"Through a clear commercial vision, a well-defined sports marketing strategy and a relentless enthusiasm within the PUMA organisation, we're proud to have signed this partnership with a truly global football club."