Glazer, also an owner of Super Bowl winners Tampa Bay Buccaneers, has completed the purchase in his role as chairman of private equity firm Lancer Capital.
The new T20 League is a new, professional six-team cricket competition authorised by the Emirates Cricket Board which will begin in February and March next year.
Glazer said: "I am very excited to be a part of UAE T20 at its formation. UAE T20 promises to be a world-class event that will be transformative to the growth of cricket in the Emirates."
The names of the franchises are yet to be announced.
Khalid Al Zarooni, UAE T20 League chairman and vice-chairman of the Emirates Cricket Board, said: "I am very excited to welcome Mr Glazer to the UAE T20 Family.
"To have a partner who has invested into sports properties with a long-term perspective is a testament to the strength of the UAE T20 League's business model and its value proposition to fans and its stakeholders, and an ode to the UAE as the destination of choice for global sports events."