The deputy was returning four prisoners to jail when one of them attacked him inside a secure area of the Jackson County Courthouse, Sheriff Stan Evans said.
"At some point, the inmate apparently obtained the officer's weapons, shot him what looks to be three times, then took control of the van," Evans said.
The inmate, who sped away with the injured deputy inside the van, got only about 100 yards before he was shot by two deputies, the sheriff said.
A hospital spokeswoman said Timothy Lemar Jones, 28, died early Tuesday at Athens Regional Hospital, where he was taken after the shooting.
Television reports showed a deputy's van crashed into a chain-link fence along a lane leading to the courthouse. The van's windshield had three bullet holes.
Deputy Kimsey Gray, a 14-year veteran, suffered gunshot wounds to the abdomen, left arm and right leg, authorities said. He was hospitalized in good condition.
The sheriff said Jones was arrested in Jefferson last week and charged with armed robbery.
The courthouse was briefly shut down after the 4:30 p.m. shooting.
Evans said the deputy had followed policy that requires inmates be transported with belly chains and leg irons and accompanied by an officer. The incident remained under investigation.
He said investigators were trying to determine whether the other prisoners had a role in the escape attempt.
Jefferson is about 60 miles northeast of Atlanta.