The 32-year-old Englishman arrives having spent the past three years with Peterborough United, during which time he was named in the League One team of the season and captained the team as they won promotion to the Championship.
Beevers said he is looking forward to playing club football overseas for the first time in his career.
"It's an idea I've been exploring for a while now," Beevers said. "It's something that I really want to do and I'm really excited about it.
"It's a brand new challenge and completely different to what I've been used to over the last 15 years in the U.K.
"It kind of all fell into place with Andy Keogh retiring and becoming head of recruitment at the club, so I had a direct point of contact with Andy.
New Glory coach Ruben Zadkovich said Beevers would bring a wealth of experience and quality to the defensive unit.
"He has a very commanding presence, is a natural leader and is very tough in the contest," Zadkovich said. "He has captained clubs at Championship level and played pivotal roles in successful teams."
But captain Brandon O'Neill has left Glory due to family reasons, despite having another two years to run on his contract.