Glasnow has been on the injured list since June 15. The 27-year-old right-hander went 5-2 with a 2.66 ERA in 14 starts.
The news was not unexpected.
Glasnow visited Dr. Keith Meister on Saturday, at which time Rays manager Kevin Cash said surgery was the likely outcome.
The decision was finalized after a follow-up examination Tuesday.
"I know he wants to be here, I know he wants to be competing, but he's got a big career ahead of him,'' Cash said after Tuesday night's game. "Most importantly it's the clarity and the peace of mind for Tyler to have the procedure, and knowing him, he'll bust it through the rehab.''
Tampa Bay leads the American League East by one game over the Boston Red Sox despite having 15 pitchers on the IL.
The Associated Press contributed to this report.