Police arrested the man after they found a "fairly compelling" chain of circumstantial evidence linking him to the incident, Mr Hudson said.
He said the man, who had indirect links to the Pulver family, would be charged with aggravated breaking and entering.
No one else was being sought in connection to the crime.
Eighteen-year-old Madeleine Pulver spent 10 hours with a fake bomb attached to her neck after a balaclava-clad intruder broke into the family's Mosman mansion and strapped it to her on August 3.
Technicians from the NSW Police Bomb Squad worked overnight for 10 hours to remove the device from the 18-year-old.
The device was found not to contain any explosives.
NSW police commissioner Andrew Scipione said Miss Pulver had been subjected to "torture" during her ordeal.
Since then, numerous media reports have surfaced in relation to the incident.
On Sunday, it was reported that police had seized a computer from Kincumber Library on the NSW Central Coast as it was believed to be connected to the note left with the Mosman teenager.
The long, typed note listed strict instructions for the 18-year-old, and made reference to the James Clavell novel Tai-Pan, but included no demands for money.
The note contained a threat to detonate a bomb if Maddie contacted police or tried to disarm it.
Last week it was reported that detectives had spoken to a man they believed to be responsible for the attack.
Police had identified the man from information gathered from Madeleine and her family, The Daily Telegraph reported.
A senior police source reportedly told the newspaper that a suspect had been spoken to by detectives but had not been formally interviewed.
Madeline's father, Bill Pulver is the chief executive of Appen Butler Hill, a linguistic software company that specialises in voice recognition software.
Since the incident the family have been urged to increase security around their home and Madeleine has shut down her account on the social networking site Facebook and ditched her mobile phone.
- AAP
