Livings, who joined the Cowboys as a free agent last offseason, started every game in 2012 at left guard but was slowed by the knee injury since early in training camp.
He joins a handful of Cowboys who have had offseason surgery.
DeMarcus Ware is rehabbing from right shoulder surgery and is expected to miss the entire offseason and be ready for training camp. According to a source, Ware will not have surgery on his right elbow.
Tight end John Phillips, who will be an unrestricted free agent, had ankle surgery, and cornerback Sterling Moore had surgery on his left knee. Both will be ready by the start of the offseason program.