His chosen conduit for terror was Interstate 65, preying on women working as night clerks at motels along the highway.

For more than three decades, the serial killer evaded the authorities, who say he was responsible for at least three murders and a separate sexual assault in Kentucky and Indiana during the late 1980s and in 1990.

Investigators now say that they have discovered the identity of the man known as the I-65 Killer, and that he died in 2013 at age 68.

At a news conference on Tuesday in Indianapolis, the authorities said that the killings were committed by Harry Edward Greenwell, who had served at least two prison sentences, in Iowa and Kentucky, for a string of violent crimes.

The breakthrough in the case was reached when genetic genealogy was used to match Mr. Greenwell’s DNA to ancestry records, according to investigators, who declined to elaborate on those findings.

Law enforcement officials said there was a distinct possibility that Mr. Greenwell was responsible for additional murders, rapes and robberies in the Midwest, which are being actively investigated.

“I hope that today might bring a little bit of solace to you, to know that the animal that did this is no longer on this earth,” Douglas G. Carter, the superintendent of the Indiana State Police, told the victims’ relatives at the news conference.

Mr. Carter said that advances in DNA analysis and the dogged work of investigators should give other criminals pause.

“The message is: You might be able to hide for a while, but we’re going to find you, even if you’re not here,” he said.

Three of the victims were sexually assaulted and shot. The motels, one in Kentucky and two in Indiana, were just off Interstate 65, a north-south highway that extends from Gary, Ind., to Mobile, Ala.

In the early morning hours of Feb. 21, 1987, the police discovered the body of Vicki Heath, 42, behind a Super 8 motel in Elizabethtown, Ky., The Courier-Journal of Louisville, Ky., reported at the time. A guest had alerted the authorities that the motel’s clerk was missing.

More than two years later, and about 300 miles north, investigators say, the killer struck again — twice in a matter of hours.

A worker at the Days Inn in Merrillville, Ind., had found the body of the night clerk, Margaret Gill, 24, in a vacant wing of the motel on March 3, 1989, according to news reports at the time.

About two and a half hours later, Jeanne Gilbert, 34, was abducted at gunpoint from a Days Inn in Remington, Ind., according to published reports. Her body was found in a ditch about 15 miles away on a road near a farm.

“In our case, we’ll never know what the killer was thinking,” Kimberly Gilbert Wright, Ms. Gilbert’s daughter, said on Tuesday during the news conference. “We’ll never learn any of the whys of his actions, and that’s just where we sit today.”

Ms. Wright thanked investigators for bringing the serial killer “out of the dark and into the light.”

“For some of us, no closure has ever taken place, and the horrors are lived on a daily basis,” she said.

About $426 had been stolen from the two motels in Indiana, which were about 45 minutes apart.

But with no witnesses to give a description of a killer, the investigation remained cold.

Then in January 1990, a 21-year-old clerk at Days Inn in Columbus, Ind., about 45 miles southeast of Indianapolis, told the authorities that she had been raped at knife point in a motel robbery that fit the pattern of the previous attacks, the authorities said.

The clerk was able to give investigators a description of her attacker, who she said had thrown coffee in her face. A sketch of the attacker, a bearded man in his late 30s to mid-40s with greenish eyes and a knit cap, was developed based on the clerk’s description.

The rendering led to dozens of leads and several potential suspects, but their DNA did not connect them to the murders, which the authorities more than two decades later had determined to be the work of a serial killer.

Mr. Greenwell, who was born in Kentucky and was in his 40s when the murders took place, had an extensive criminal past, the authorities said.

A timeline provided by the Federal Bureau of Investigation on Tuesday showed that he was arrested on armed robbery and sodomy charges in Kentucky in 1963 and 1965. He was paroled from the Kentucky State Penitentiary in 1969.

In 1982, he was arrested on burglary charges in Iowa, where he twice escaped from custody and was recaptured. That same year, he was sentenced to prison in Iowa, but was released in 1983. He died of cancer in Iowa in 2013, law enforcement officials said on Tuesday, citing Mr. Greenwell’s obituary.

The breakthrough in identifying the so-called I-65 Killer adds to the list of cold cases that have been solved as a result of genetic genealogy. The process, which involves crosschecking DNA evidence with ancestry records, has been instrumental in identifying dozens of suspects in languishing cold cases, most notably the so-called Golden State Killer in California.

Investigators said that they had preserved a wealth of evidence from each of the crime scenes in Kentucky and Indiana that included DNA, ballistics, hair and clothing fibers. In 2019, an F.B.I. task force became involved in the case, which is when efforts focused on using genetic genealogy to identify the serial killer, said Herbert J. Stapleton, the special agent in charge of the F.B.I.’s Indianapolis field office.

“I know that this announcement can’t take away the pain that you felt at this loss,” Mr. Stapleton said. “But what we hope is that through today’s information and revelation, this provides some answers that may aid you in your healing process that you go through every single day and bring you some sense of peace.”

Susan Campbell Beachy contributed research.