"We couldn't be any more thrilled to let everyone know that his surgery went perfect," the family said on the Instagram account set up to provide updates on his progress. "The doctors are very happy with the outcome, and we are so grateful."
Oliverson will remain in the pediatric intensive care unit overnight.
Wayne Sterling and Amir Vera of CNN noted Oliverson was airlifted to the hospital after he fell from his top bunk bed at the dormitories set up for the Little League Baseball World Series in Williamsport, Pennsylvania, on August 15.
His father said the 12-year-old, who was previously placed in a medically-induced coma, was "fighting for his life."
Sterling and Vera also noted Oliverson fell and hit his head a second time Saturday night, but a CAT scan returned "normal" results Thursday.
Oliverson was at the LLBWS as part of the team from Utah. The team was the Mountain Region representative.
Little League allowed his brother, Brogan, to join the team as a replacement player.
The Mountain Region representative lost to the Southeast and Midwest representatives and was eliminated from the tournament.