Kermit Bryson died Friday around 12:30 a.m. at Erlanger Hospital in Chattanooga, house supervisor David Trillet said.
Tennessee Bureau of Investigation director Mark Gwyn said agents found Bryson behind his girlfriend's house Thursday evening and negotiated with him for about 20 minutes before he shot himself in the head.
Federal, state and local authorities launched a manhunt for Bryson after the Thursday morning shooting death of Grundy County sheriff's deputy Shane Tate, 28.
Gwyn said officers did not fire any shots during the negotiations in Monteagle, a town of 1,200 people along Interstate 24 about 35 miles northwest of Chattanooga.
"We gave it the best effort we could," Gwyn said.
Tate died at a mobile home where he was trying to take Bryson into custody on a probation violation warrant.
Officers had been looking for Bryson for six to eight months when they found him around 3 a.m. Thursday at a mobile home in Monteagle.
Shots were fired and Tate died at the scene, Gwyn said.
Monteagle Police Officer Brian Malhoit was grazed by a bullet but not seriously hurt. A reserve deputy also at the scene wasn't injured.
Gwyn said there were other people in the home at the time of the shooting, although he declined to identify them.
Within hours of the shooting, armed officers were using dogs and helicopters to comb the rugged area at the southern end of the Cumberland Plateau in what TBI spokeswoman Kristin Helm described as "an absolute all-out manhunt."
A neighbor and longtime friend of Bryson's said shooting someone would be out of character for him.
"He's not a bad guy. He had to freak out in some way," said Tim D. Sanders, 30, before authorities found Bryson.
Sanders said he and Bryson spent weekends in jail together last summer and that the slain deputy was the jailer. He said Tate and Bryson were friendly.
Bryson's criminal record includes convictions for theft, burglary and a jail escape in 2001.
Grundy County Mayor Ladue Bouldin said Tate was married with five young children and had graduated from Tennessee Law Enforcement Training Academy just two weeks ago.
Probation officials said the warrant was issued for Bryson because he failed drug screens and violated curfew while on probation for a 2007 felony marijuana possession charge.
Helm said the three officers approached Bryson's mobile home carefully and made their way inside. Officers often serve warrants early in the morning, expecting that suspects will be asleep.
"The officer was actually shot inside the residence," she said.
Bryson's former mother-in-law, Marcia Crowe, said Bryson was married to her daughter for about a year before they divorced several years ago, and they have a 10-year-old daughter.
"I saw it on TV and I just couldn't believe it," Crowe, a 57-year-old from Dayton, said in a phone interview Thursday. "I expected him to steal, do dope and stuff like that, but I never thought he would kill someone."
Brian Grisham, director of the training academy, called Tate a good officer and person.
"He seemed enthusiastic about what he was about to do," Grisham said.