Another deputy, Patrick Rohrer, was also killed during the incident, officials said. King had 13 years of service and Rohrer had been with the department for seven years.
Major Kelli Bailiff, of the Wyandotte County Sheriff's Office, said it was possible the deputies were shot with their own weapons.
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King had three children, Bailiff said, and Rohrer had two.
Details remain sketchy about what happened, but somehow the deputies were overcome by one of the inmates and shot.
Wyandotte County sheriff's spokeswoman Maj Kelli Bailiff said the suspect was wounded in the shooting that took place outside the Wyandotte County courthouse shortly after 11am Friday morning. Both of them were parents, according to authorities. The two had a combined 20 years of service for the sheriff's department in Wyandotte County.
Wyandotte County Courthouse in Kansas.
A candlelight vigil for the deputies will be held at 8 p.m. Sunday in front of City Hall. "It's a tremendous, great loss to our agency".
"Yesterday was a terribly tragic day for two of our young, bright, committed sheriff's deputies, Theresa 'T.K.' King and Patrick Roher", the mayor told reporters at a press conference Saturday, before holding a moment of silence to honor the slain deputies.
Kansas City, Kansas has dealt with other officer shootings in the recent years.
Bailiff said the investigation into what happened is continuing, but the officers followed the established protocol for transporting inmates.
'Our hearts break for our brothers and sisters at Wyandotte County Sheriff's Office as well as for the loved ones of the deputies shot today, one of whom has died.
"It seems like Wyandotte County has really been hit hard recently", she said.
The year before, Wyandotte County Sheriff's Deputy Scott Wood was shot at a convenience store but survived. Bailiff said the second inmate, who was not identified, was unharmed.