(CNN) -- A 50-year-old man accused of strapping a suspected explosive device around the neck of an 18-year-old woman near Sydney, Australia, earlier this month was arrested Monday more than 9,000 miles away, Australian law enforcement officials said.
"We are enormously relieved that an arrest has been made," Bill Pulver, the alleged victim's father, told reporters. "These past two weeks have been a very difficult time for us."
Elizabeth Fries, special agent in charge of the FBI's division in Louisville, Kentucky, announced Monday night that the man detained is Paul Douglas Peters. He was arrested "without incident" around 4 p.m. ET (6 a.m. Tuesday in Sydney) in his ex-wife's home near LaGrange, about 25 miles (40 kilometers) northeast of Louisville.
Police believe Peters is the man who broke into the Mosman, Australia, home of the woman, later identified as Madeleine Pulver, on August 3 while she was studying for her year-end exams. There, he attached what she believed to be a bomb to which he attached a letter with "financial demands," New South Wales Detective Superintendent Luke Moore explained Monday from Kentucky.
The woman spent 10 hours attached to the device before having it removed by police bomb technicians. Authorities later determined it had been inert, and -- while the letter noted there would be follow-up instructions -- police did not talk with the perpetrator at the time.
The case subsequently drew intense media attention in Australia, and prompted police to launch an extensive investigation.
That probe led to Peters' arrest Monday by FBI agents working "very, very closely" with their Australian counterparts, said New South Wales police commissioner Andrew Scipione. Moore said that police got information last week leading them to the suspect, who was believed to be alone when he was arrested.
"The information that I have is that the suspect was surprised" to be arrested, said Assistant Commissioner David Hudson.
Hudson said that the suspect is an Australian citizen who frequently traveled to the United States on business, and Moore added that he has "family connections" in the country and had previously lived here. He had been in Sydney, which is his primary place of residence, for a six-week stretch before flying to the United States on August 8, said Hudson.
Hudson said Peters was not yet a suspect when he flew overseas. But "a fairly detailed chain of circumstantial evidence" -- including a description from the victim, even though the alleged assailant was "heavily disguised" -- ultimately led them to the United States and the arrest.
There were "some links between the suspect and the family; however, no direct links," said the assistant commissioner, who declined to elaborate, citing the ongoing investigation. But a short time later in Kentucky, Moore stated he is "certainly not known to the Pulvers and, at this stage, we're still exploring what the link is."
The assistant superintendent added that Australian authorities "do not believe" Peters' former wife had any knowledge of the alleged collar bomb incident in Mosman.
Peters is expected to be arraigned Tuesday morning in a U.S. court in Louisville, said Moore, one of two New South Wales police members who flew overseas Sunday night. Australian authorities plan to seek his extradition back across the Pacific Ocean.
The alleged crime occurred in Mosman, a wealthy suburb about eight kilometers (five miles) from Sydney where many well-connected people, sports stars and celebrities live, resident and Australian news reporter Dave Kirwan told CNN.
When the alarm was first raised, he said, many residents locked themselves in their homes fearing they might also be in danger.
"This kind of thing doesn't really happen here," Kirwan said at the time.
Speaking on what was Tuesday morning in Australia, Scipione thanked Madeline and the rest of the Pulver family, as well as investigators in both Australia and the United States, for overcoming numerous challenges to find the person they believe was behind this "hideous crime."
"The motto for (the New South Wales police force) simply says, translated, 'Justice swiftly follows crime,' " said Scipione. "You've seen that today."