Klaas, 32, was found sexually assaulted, strangled and left unconscious in her Hermosa Beach home on Jan. 30, 1976, according to the L.A. County Sheriff's Department. She was taken to a hospital, where she lay in a coma for five days before her death several days later.
Kenneth Troyer was named as the murder suspect during a news conference attended by Medley and other family members.
Troyer had escaped from the men's prison in San Luis Obispo in 1982 and during that time out of prison was identified as a suspect in several sexual assaults and robberies, according to Los Angeles County Sheriff Jim McDonnell. During an attempt to capture him in March 1982, law enforcement officers shot and killed him,, McDonnell said.
He was identified by a familial DNA search, a technology in which investigators scour law enforcement databases to find possible relatives of an individual suspected of a crime. Troyer was linked to the murder case through a DNA sample collected six years ago from a "first-degree" relative, sheriff's Capt. Steve Katz said.
The captain declined to specify the family member's relationship with Troyer, but said a father or son is an example of a first-degree relative.
Medley, best known as one of the Righteous Brothers with former singing partner Bobby Hatfield, thanked those who had worked for years to solve the case.
"It's been a long road, and we're just thrilled that we can close the book on this," Medley said, adding that he "became numb" when he initially learned the suspect's identity had been discovered.
Klaas remarried after her marriage with Medley. She and her new husband had a child who was 4 years old in late January 1976. Klaas dropped off the child at daycare and went home on the day of the fatal attack, authorities said.
When neighbors were unable to contact her, they became concerned and notified police. A man was seen leaving her home at the time but Klaas' killer was never located. Investigators ruled out her husband as a suspect.
McDonnell praised the tenacity of homicide detectives who continued to work the case even after an initial familial DNA search in 2011 proved fruitless. Investigators were able to name Troyer as the killer after requesting another search last year, the sheriff said.
"The familial DNA search is the only reason Troyer was identified in this horrific crime," he said.
CORRECTION: An earlier version of this story identified Jim McDonnell as the Orange County sheriff, but he is the Los Angeles County sheriff.