(CNN) -- A 63-year-old man accused of sexually assaulting and impregnating his young relative is in federal custody, following his arrest three decades after and about 1,800 miles from where the alleged crime occurred.

Deputy U.S. Marshals and law enforcement officers in Kentucky arrested James David Gibson on Wednesday, about two years after his alleged 13-year-old victim came forward to authorities.

She waited several decades to tell her story because, at that point, her daughter was an adult and she felt that both were old enough to defend themselves, U.S. Marshals spokesman Chris DeRosa said Thursday.

"She didn't tell anyone leading up to that, for fear of her life and her child's life," said DeRosa.

The alleged assaults occurred in the late 1970s and early 1980s in Benson, Arizona, according to the U.S. Marshals Service. Authorities said that, after learning that the victim was pregnant, Gibson kidnapped her and together they fled to Tennessee.

It was not until 2009 that the victim came forward and law enforcement authorities opened their case. By then, she was back in Arizona, more than 1,500 miles from Gibson. It wasn't immediately clear when the two separated.

Soon thereafter, Gibson was tracked down in Tennessee. After he refused to provide a DNA sample, law enforcement tried to serve him a court order demanding as much. But by then, he'd fled the state -- prompting a warrant, issued in March of 2009, charging him with kidnapping and sexual assault of a minor, according to the U.S. Marshals.

Gibson was eventually found again in Jenkins, Kentucky, where he was living with a granddaughter.

By Thursday, authorities were awaiting clearance to extradite Gibson back to Arizona. The U.S. Marshals' office was not aware if, at that point, he had yet retained or been assigned an attorney.

CNN's Greg Botelho and Marlena Baldacci contributed to this report.