For 50 years, a macabre mystery loomed over the small town of Boone, N.C., where the bodies of three family members were found in a bathtub during a snowstorm in 1972.

The unsolved murders of Bryce, Virginia and Bobby Durham flummoxed investigators, who chased various leads over the decades that never led to a suspect.

But this week, the Watauga County Sheriff’s Office announced that it had solved the triple homicide, which it described as a hit by a criminal network called the Dixie Mafia. In 2012, the F.B.I. described the group as a “loose confederation of thugs and crooks who conducted their criminal activity in the southeastern United States.”

Investigators said they connected the group to the killings after receiving a tip in 2019, when a sheriff in Georgia told them he had been contacted by a son of one of the assailants. The son was doing research for a book on the murderous ways of his father, Billy Sunday Birt, who died in prison in 2017 while serving a life sentence for three murders that he committed in the 1970s.

Sheriff Len Hagaman of Watauga County identified Mr. Birt and three other men — Billy Wayne Davis , Bobby Gene Gaddis and Charles David Reed — as the killers in a statement on Tuesday.

“We are confident that we now know who committed these crimes,” Sheriff Hagaman said in the statement. “This is a much-needed turning point for the Durham case.”

Mr. Davis, 81, the only suspect in the Durham killings who is still alive, is already serving a life sentence in a Georgia prison for another murder, according to Sheriff Hagaman.

It was not immediately clear whether Mr. Davis had a lawyer. He is serving a life sentence at the Augusta State Medical Prison for a 1971 murder in Douglas County, Ga., according to the Georgia Department of Corrections, which did not immediately respond to a request for information on Wednesday.

Investigators said this week that they had not been able to determine who had hired the men to kill the Durhams. The family owned a Buick dealership in Boone, in the Blue Ridge Mountains near the Tennessee border.

When reached on Wednesday, Sheriff Hagaman did not comment further on the case or explain why the family might have been targeted.

In a statement released through the Sheriff’s Office, Ginny Durham, whose parents and brother were killed, thanked investigators for continuing to pursue the case.

“I know that they sacrificed many days and weekends in order to work on solving this case since 1972,” she said. Efforts to reach her on Wednesday for additional comment were not immediately successful.

On Feb. 3, 1972, the bodies of Bryce Durham, 51; his wife, Virginia, 44; and the couple’s son, Bobby, 18, were discovered by their son-in-law at the time, who the authorities said had gone to check on them.

Ms. Durham had been strangled, while Bryce and Bobby Durham had been strangled and drowned in the bathtub, The Watauga Democrat reported. At the time of the killings, The Charlotte Observer reported that the couple’s son-in-law told investigators that Ms. Durham had called him to say that some men were holding her husband and son captive in the house.

A breakthrough in the cold case came in 2019, when Mr. Birt’s son, Shane Birt, spoke to a sheriff’s deputy in White County in northeastern Georgia while doing research for a book project about his father and mother, investigators said.

Phil Hudgins, the author of an upcoming book about Mr. Birt’s father and mother, said the younger Mr. Birt had described the time his father was nearly apprehended after killing someone in North Carolina.

“Shane remembered his dad almost getting caught in a snowstorm in the mountains of North Carolina,” Mr. Hudgins said on Wednesday.

The Georgia deputy who received the initial tip about Mr. Birt’s role in the North Carolina killings and is now retired did not immediately respond to a request for comment on Wednesday.

Rufus Edmisten, a Boone native who was North Carolina’s attorney general from 1974 to 1984, said on Wednesday that he had become preoccupied with the case over the decades. He recalled meeting Bryce Durham’s mother, who he said had pleaded with him to find the killers. She has since died, he said.

“She said that before she died she would love to see this case solved,” Mr. Edmisten said, adding, “I didn’t want to let her down.”

Mr. Edmisten said it was frustrating not to be able to give her closure, but he credited the sheriff and other investigators with following through with the investigation.

Just the same, the breakthrough came as a great relief, he said.

“It has been the mystery of the mountains,” he said, “for years and years and years.”

Mr. Hudgins said that Shane Birt wanted the truth to emerge about his father, who died of suicide at 79.

“He told me that if he could apologize to every single victim of Billy Sunday Birt, he would,” Mr. Hudgins said. “He’s not trying to glorify his father. His father was indeed a murderous man who killed dozens of people. He wants to provide closure to a lot of people.”