"They're happy with the progress of the entry process, and now [doctors] can begin to get rid of the tumor," the figure skater's rep, Michelle Thornbury, tells PEOPLE of the procedure, which was completed late Wednesday.
Hamilton, 51, had the surgery in Boston, where he is surrounded by family, including his wife Tracie, their friends and his brother Steve. "They're all feeling the love coming from all of us," the rep says.
After the surgery was complete, Hamilton's rep told PEOPLE, "Scott is resting comfortably and expected to make a full recovery. He and his family are so thankful to the doctors and surgical team for taking such good care of him and grateful to everyone for their thoughts and prayers."
He will remain in ICU for a couple days and is expected to return home next week.
In 2004, Hamilton first discovered he had the tumor, called craniopharyngioma. Although benign, if left untreated it could have caused him to go blind. He chose to treat it with Gamma Knife, a procedure that bombards the tumor with high, pinpoint doses of gamma radiation. At the time, doctors were able to virtually destroy the tumor.
After that procedure, Hamilton, who also underwent chemotherapy for testicular cancer in 1997, was upbeat about his life with son Aidan, now 6, and his wife, Tracie. (The athlete and his wife have another son, Maxx, born in 2008.)
"You think you love your life, but you're just scratching the surface," he told PEOPLE. "Now I look at my son and I realize I may not be able to spend much time with him. So my level of appreciation for what I've got now has gone to a whole other level."