The team said the so-called "Tommy John operation" was successful and that the 23-year-old left-hander will miss the remainder of the season as well as part of the 2012 season.
Anderson complained of soreness in his left elbow after pitching June 5 and was placed on the 15-day disabled list two days later, his third trip to the disabled list.
He was 3-6 with a 4.00 ERA in 13 starts.
The surgery was performed by Dr. James Andrews in Pensacola, Fla.
Kate Moss Playboy shoot is classic Playboy, classic Kate
Exploding whale video goes viral on Internet