Investigators used fingerprints to identify the man as Travis Trim, 23, State Police Maj. Kevin Molinari said.
It wasn't immediately clear if Trim died in the shootout with troopers earlier Wednesday or in the fire that broke out when police fired tear gas canisters into the house later in the day. Molinari said an autopsy was planned Thursday afternoon. Fire officials were still searching the home.
"I can't tell you whether he was dead or alive when the fire started," said Preston Felton, acting superintendent of the New York State Police.
The pursuit began Tuesday after a trooper stopped Trim in a stolen minivan in the Margaretville area, about 65 miles southwest of Albany at the edge of the Catskill Mountains.
When Trim failed to provide identification, Trooper Matthew Gombosi told him he was under arrest, Felton said. Trim then pulled a handgun from his waistband and shot Gombosi, Felton said. Gombosi's body armor kept him from being seriously injured, but the suspect escaped, police said.
Police found the stolen Dodge Caravan abandoned on a road in nearby Middletown.
The farmhouse where Trim apparently holed up, in a hamlet called Arkville, was described by neighbors as a weekend residence.
Wednesday morning, state troopers were searching the area when two more were shot, Felton said. Trooper David C. Brinkerhoff, 29, was shot in the head and died shortly afterward. Richard Mattson was in serious but stable condition with a wound to his arm.
The fire erupted soon after an armored vehicle rolled up and police fired tear gas into the farmhouse. SWAT teams tried to enter the home but were driven back by the flames.
Felton said that police used a "non-incendiary type" device containing tear gas and that it was possible Trim set the fire.
The home's owner, Rommel Aujero, was aware that it burned and "appears to be a very understanding man," Felton said. A phone number for Aujero could not be located.
Trim is from North Lawrence, about 10 miles from the Canadian border. He has a 2005 conviction for driving while intoxicated and aggravated, unlicensed operation, but his grandmother said he had tried to turn his life around.
"He wanted to go to college. We talked to his probation officer to help fix it up," Ruth Trim said in a telephone interview from her home in Dickinson Center. "I'm devastated. He was going to go to college to make something of himself. Now, he's really ruined his life."
Trim had been enrolled briefly at the State University of New York-Canton but withdrew in November, said Randy Sieminski, a school spokesman.
He had been arrested on charges of marijuana possession and providing alcohol to a minor while at SUNY-Canton, but his family and officials at schools he attended were stunned to hear he was a shooting suspect.
"It's all so bizarre," said Mark Hill, a SUNY-Canton instructor who had Trim in a freshman class. "He had no bad dealings here. He got along with everyone and worked well in team settings."
Last summer, Ralph "Bucky" Phillips led police on a five-month manhunt throughout western New York after breaking out of a county jail. He shot one trooper during a traffic stop and two others who were searching for him. One of those troopers died.
Phillips was captured in September and is serving two life sentences.