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.
'Deceptive' communication
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.