Paul Douglas Peters, 50, was arrested by the FBI Monday at his ex-wife's home north of Louisville.
The arrest came nearly two weeks after authorities say a masked man broke into a luxury home in Sydney, chained a device to 18-year-old Madeleine Pulver's neck, and left a note.
Pulver spent 10 hours chained to the device before she was freed and it was found to be fake. Monday's arrest came as great news to Pulver's father, the CEO of a software company.
"This has been a baffling and frightening experience," said Pulver's father William. "We are hopeful that this development marks the beginning of the end of this traumatic ordeal for our family."
"There were a range of pieces of evidence that led us to identifying this suspect," said Luke Moore from New South Wales police.
Investigators believe the attack was part of an extortion attempt. Peters' extradition hearing is scheduled Oct. 14.
In Australia he faces charges including kidnapping, as well as breaking and entering.
The Associated Press contributed to this story.