The archdiocese says Brunett, 79, is in critical but stable condition in the hospital's intensive care unit.
"He's responding well to voice commands and to those around him," archdiocese spokesman Greg Magnoni tells KOMO Newsradio.
He said Brunett was golfing with a friend when he suffered the stroke. After Brunett's successful surgery, current Archbishop J. Peter Sartain administered the anointing of the sick to him.
Magnoni said Brunett's stroke came as a surprise to those who know him.
"He had been in good health. He's always been an extremely active person," Magnoni said. "Recently he had a little back spasm problem, but other than that he has always been a robust and vigorous person, so it comes as quite a surprise to us."
Brunett served as archbishop of Seattle from 1997 to 2010.
Visitors are not being allowed to see him for the time being, hospital administrators said.
Magnoni said several parishes in the archdiocese are planning masses and times of prayer for the former archbishop's speedy recovery.