The 59-year-old Stewart, who compiled a 28-12 record over four seasons at the helm of the Mountaineers, was taken by ambulance from Stonewall Resort near Roanoke to a local hospital, where he was pronounced dead, the officials said.
He is survived by his wife Karen and son Blaine, who is completing his junior year at Morgantown, W.Va., High School, The Charleston Gazette reported.
"He was a compassionate, energetic, and kind person," WVU President Jim Clements said. "He loved his family dearly and was extremely community-oriented and very giving of his time. He will be greatly missed."
The school said Stewart was golfing with former WVU Athletic Director Ed Pastilong when he succumbed.
Stewart took over the head football job following the departure of Rich Rodriguez to Michigan before the end of the 2007 campaign.
He resigned in June 2011 following accusations he had tried to steer reporters into probing the personal life of current Coach Dana Holgorson, who was then the team's offensive coordinator.