Padres general manager Josh Byrnes confirmed that plan on Friday morning.
Kelly is expected to miss 12 to 18 months rehabbing after the procedure.
Kelly said on Monday that doctors found small tears in his right ulnar collateral ligament. He was having pain during a March 7 spring outing, which prompted a closer examination the following week.
Kelly was shut down due to elbow pain twice during the 2012 season.
He was 2-3 with a 6.21 ERA in six starts last season and was a candidate for this season's starting rotation.