Williams had surgery to remove a tumor from his right kidney on Sept. 19, which was also an oncocytoma, which is often indistinguishable from kidney cancer on x-rays.
Dr. Eric Wallen, professor of urology at UNC said as a result of the biopsy, Williams will not require surgery on the left kidney.
"The result of the biopsy of the tumor on the left side is great news for Coach Williams and his family," said Wallen. "He is recovering very well and we will continue to follow his progress. In the meantime, he can return to his normal schedule, including the team's first practice on October 13."
"Once again, I want to say how overwhelmed my family and I are by the support and concern of so many former players, members of the Tar Heel family and friends and fellow coaches from around the country," said Williams. "Saying I'm overwhelmed truly doesn't give justice to how much I appreciate all their thoughts and good wishes. The support has been off the charts.
"The level of professionalism, compassion and care that the entire medical team at UNC Health Care provided to my family and me has been extraordinary. Dr. Wallen and his staff have helped us get through a difficult process better than I ever could have expected.
"I also want to thank my family, especially Wanda, Scott, Kim and Katie, and my staff and players, for helping me get through these last three and a half weeks. The degree to which their love and support helped me is something I will never be able to adequately express."