Williams, 62, was found to have a tumor on his kidney during a physical examination this month. Doctors said the procedure to remove the tumor went "according to plan."
The school said Wednesday Williams might have an operation on his left kidney next month but he is expected to have recovered by the time of the Tar Heels' first game Nov. 9.
"Coach Williams did great," said Dr. Eric Wallen, a professor of urology at the university, who led the surgical team. "I fully expect him to coach this season and for years to come.
"He could miss some practice time if we perform another procedure sometime in October but he would be able to resume his coaching duties prior to the start of the regular season."
Williams is in his 10th season at North Carolina. He has a 257-68 record with the Tar Heels, winning the NCAA tournament on 2005 and 2009. Prior to joining North Carolina, his alma mater, Williams' first head coaching position was at Kansas, where he built a 418-101 record.
He was inducted into the College Basketball Hall of Fame in 2006 and the Basketball Hall of Fame in 2007.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
18-year-old elf alleges mall Santa pinched her buttocks on the job