The bodies have not yet been identified, said Telfair County Sheriff Chris Steverson. He said the couple's car was also found submerged in a nearby lake.
"It's not the outcome we had hoped for but, obviously, it's the one we have to deal with," Steverson said. "We'll analyze the vehicle, the bodies and hopefully we can come to some conclusion as to how they met their fate."
Earlier Monday, the suspect sought in the case who had posted a Craigslist ad turned himself in, the Telfair County Sheriff's Office said on its Facebook page.
Authorities have said that Ronnie "Jay" Adrian Towns, 28, was wanted on charges of giving false statements and criminal attempt to commit theft by deception. His family was integral in securing his surrender, Steverson said.
Elrey "Bud" Runion, 69, and his wife, June, 66, placed an ad looking for a 1966 Mustang on the advertisements website and contacted a car seller on Craigslist.
They drove to the South Georgia town of McRae from Marietta, an Atlanta suburb, on Thursday to meet someone who responded to the ad, relatives said.
No one has heard from them since.
"He was excited about the car. He had one when he got back from Vietnam," daughter Stephanie Bishop told CNN affiliate WSB-TV
Asked whether Towns owned a Mustang like the one the Runions were looking for, Steverson replied, "He does not. We feel that the entire communication he had with Mr. Runion was deceptive."
Relatives filed a missing persons report after the couple failed to show up to baby-sit their grandchildren the next day.
'Last known communications'
Towns, 28, had the "last known communications" with Runion, Steverson said.
Towns turned himself in just before noon Monday. He "is currently in custody and no further details are available at this time. Details will be posted as they become available," the Facebook page
for the Sheriff's Office said.
It was unclear when his bond hearing would be held, Steverson said.
The couple made the trip to look at the car, and once Runion got to Telfair County, the suspect communicated with him, according to the sheriff. He did not say who called whom. McRae is about 180 miles from Marietta.
"Early on in the investigation we did contact Mr. Towns, and we did interview him and by the information he provided we found it to be false and deceptive," the sheriff said shortly before Towns turned himself in. "After we interviewed him, our efforts to contact him were unsuccessful. Today we've contacted his family, and they've been helpful in locating him."
'They are selfless'
For days, authorities searched for the couple using helicopters and watercraft, Steverson said.
Deputies contacted land owners and hunters familiar with the area in case they had seen anything suspicious.
The FBI and Georgia Bureau of Investigation assisted with the search.
"I am eternally grateful for the prayers that have been lifted up, the encouraging words, complete strangers who have reached out, we are so thankful for that," said Josh Patterson, the couple's son-in-law.
"Bud is a veteran. He and June are great people; they give so much, they are selfless."
The Runions were last seen driving a champagne 2003 GMC Envoy, which is the vehicle authorities have since recovered.
Site has history
Though the overwhelming majority of Craigslist transactions occur without incident, the site has a history of being co-opted by criminals.
Just in recent years, there have been numerous such instances. In Henderson, Nevada, police said a man placing an ad in July
met three men at a park, who took him to a vacant house, tied him up, beat and robbed him, then escaped in his car.
In March, a San Jose, California, woman responding to an ad for a cellular phone was allegedly kidnapped at gunpoint
by two men who drove her to an ATM and demanded her passcode, police told a newspaper.
In May 2013, a Maine teenager drove to Portland to sell his BMW sedan to a 29-year-old who had responded to his Craigslist ad. The teen was allegedly forced into his own trunk and driven to Delaware, according to media reports
and an FBI affidavit