Struan was the fictional British carpetbagger who made a fortune in 19th century Hong Kong in the 1960s novel Tai-Pan by James Clavell.
The bomb was a hoax, and police said that the case was being treated as extortion.
After the arrest was announced Madeleine's millionaire parents, Bill and Belinda Pulver, told a media conference of their relief. "This has been a baffling and frightening experience," Bill Pulver said. "It has tested us all."
Pulver is chief executive of a voice recognition software company who had previously lived with his family in the US where he was head of an audience ratings company.
He said the family had been overwhelmed by the love and support shown by friends, neighbours and the local community and praised the "amazing and inspirational" professionalism of the police and emergency services.
"We have been humbled by the selflessness and generosity of those wanting to help Maddie in any way they can. From those we know well, to those we have never even met before, in Australia and overseas, we want to say a very heartfelt thank you."
The Daily Telegraph said Madeleine's alleged attacker had lived in Copacabana on the New South Wales central coast and had been arrested at the five-bedroom La Grange home of his former wife, about 50km from Louisville.
Police Assistant Commissioner David Hudson told reporters yesterday that Peters was not directly known to the Pulver family and was not believed to have previously been inside their home, but some links were being investigated.
He said Peters had been in Australia for six weeks before the hoax but had not become a suspect until he later left for the US and was placed under surveillance.
"It's a fairly detailed chain of circumstantial evidence ... We'll be alleging through the courts that [Peters] was responsible for entering the Pulver home and placing the device around Madeleine's neck."
Peters is a father of three who was educated at The Scots College in Sydney's Bellevue Hill. On LinkedIn, Peters says he is the former Malaysia managing director of Australia's Allco Finance Group.
After Allco failed in 2008 during global financial crisis, he set himself up as managing director of Douglas Corporation, specialising in arranging and structuring sophisticated asset-based financial products.
The profile also says he spent eight years to 2006 working for US-based asset finance firm Connell Finance Inc and holds degrees in economics and law from the University of Sydney.
An old schoolfriend told the Sydney Morning Herald that Peters was "volatile, but he was a decent, smart guy ... I genuinely felt he meant well and wanted to do the right thing ... [these allegations are] completely out of character."
- Additional reporting: AAP
