The procedure will be performed by Dr. James Andrews, the team announced Tuesday. Moore is the first Rays pitcher to undergo Tommy John surgery since Jason Isringhausen in June 2009.
"I can't help out on the competitive side of this business right now," Moore said in the Tampa Bay clubhouse Tuesday. "This is my first significant injury where I'm going to be missing a lot of time."
Rays manager John Maddon believes Moore's decision will be beneficial in the long term for the pitcher and the team.
"It's awful, but it's great," Maddon said. "It's awful that we're going to miss this guy for a bit. It's good for him to be able to get past this moment and look forward to a really long and prosperous career. Almost all of the time, percentage-wise, it's a very successful operation."
Moore hasn't pitched since walking off the mound with elbow soreness on April 7 in Kansas City. He was placed on the disabled list the following day.
"It was an injury that I didn't think would be my ligament. I didn't think it was going to be something like that," he said. "It just didn't feel that severe."
After throwing a ball Monday, Moore realized surgery was inevitable.
"I don't think there was a whole lot of hesitation," he said, noting that he felt pain "on every single pitch."
Moore also experienced elbow soreness last season while going 17-4 with a 3.29 ERA. He was 0-2 this year despite allowing only three runs in 10 innings.
"It's tough," starter David Price said. "They're going to be working hard. They're going to be trying to get back here. Whenever they do, it's going to be a good little shot in the butt for us, and that's what you need throughout the season."
Maddon already has been forced to improvise his rotation. Left-hander Erik Bedard was going to start for the Rays on Thursday, but because of the rainout, Price will take the mound in the series opener against the New York Yankees.
Several pitchers have been diagnosed with torn elbow ligaments, requiring Tommy John surgery, since the start of spring training, including Braves right-handers Kris Medlen, Brandon Beachy and Cory Gearrin; Diamondbacks ace Patrick Corbin; Athletics starter Jarrod Parker; Mets closer Bobby Parnell; Royals setup man Luke Hochevar; Tigers reliever Bruce Rondon; and Pirates top prospect Jameson Taillon.
The Associated Press contributed to this report.