The American businessman, who acquired ownership of the club between 2003 and 2005, passed away this morning.
A statement on the website of the Buccaneers said: "The Tampa Bay Buccaneers are saddened to announce the passing of owner/president Malcolm Glazer earlier this morning at the age of 85.
"Known among his league peers as a pioneering thinker, Glazer infused his team and employees with the determination and dedication to be the best in the NFL. Glazer's commitment to building a championship organisation has provided the foundation for continued success, on and off the field."
As well as owning sports teams, Glazer also had business interests in oil, broadcasting and banking.