Renowned surgeon Dr. James Andrews will perform the procedure in Pensacola, Fla.
General manager Brian Cashman on Thursday said Chamberlain, who has a torn ligament in his elbow, would miss approximately 10 to 14 months.
"This sucks," Chamberlain said Thursday. "There's no way to sugarcoat it. It's something I didn't expect with no pain. The most frustrating part is not being there for the team. [But] everything happens for a reason. I'll come back and be even stronger."
Surprisingly, Chamberlain said he feels "no pain" and has "no idea" how the injury occurred. But he felt tightness after throwing long-toss on Tuesday and went in for an MRI on Wednesday, which revealed he had a strained flexor tendon.
Chamberlain was placed on the 15-day disabled list on Wednesday, but a dye contrast MRI on Thursday morning revealed that the injury was more significant.
"I was just trying to get out of there before I broke down," Chamberlain said of his reaction to the devastating news. "I shed a couple tears. [But] you can't let it beat you. You gotta get stronger and get better."
Chamberlain's MRI results were sent to Andrews, who confirmed that he needed to undergo Tommy John.
Soriano, who was signed for three years and $35 million this offseason, has been a major disappointment and is on the disabled list with right elbow inflammation.
Soriano has not started throwing yet, Girardi said, and is not close to returning. David Robertson will be the Yankees eighth-inning man for now, Girardi said.
Girardi said the team is "confused" by Chamberlain's injury because the reliever has not experienced any of the typical symptoms of pitchers who need Tommy John surgery.
"He said [Wednesday] was a normal long-toss for him so it really has us all kind of scratching our head," Girardi said on Thursday. "When you talk about the symptoms that someone has when they hurt that ligament, Joba doesn't have them."
When asked about the extent of the injury on Wednesday, Chamberlain said: "If you asked me to pitch today, I would tell you I could pitch today."
On Thursday, Girardi added, "He has no idea when this happened."
Before the latest diagnosis, the Yankees thought Chamberlain would sit two weeks to a month and then start a throwing program, Girardi said.
The 25-year-old Chamberlain had emerged as the team's setup man in the absence of right-hander Soriano and in 28 2/3 innings had 12 holds and a 2.83 ERA. The Yankees placed rules on Chamberlain to limit his innings in 2009, when he was used as a starter.
"If there were no 'Joba Rules' in place, could it have possibly happened earlier? I don't know," Girardi said. "There's no exact science because everybody is different."
Mike Mazzeo is a regular contributor to ESPNNewYork.com.