The victim had been home alone when the man knocked on her door claiming to be looking for his daughter just after 6am on Friday.
Police said today the victim had been informed of the arrest and that she was being comforted by family members.
"She has been incredibly brave and is holding up as well as can be expected,'' police said in a statement.
Wellington Police also thanked the local community for their support during the investigation.
"Police would like to reassure the community that events such as that which occurred in Waitangirua are rare however the public should always take a commonsense approach to personal security.
"With all communities, we would encourage everyone to look out for their neighbours and if they see anything suspicious please report it to police immediately."
Mr Basham said the arrest was a good result for police and also for the Waitangirua community.
"I hope now that the good people of Waitangirua and the wider Porirua community, with this result in mind, can get back to and feel safe in their homes and communities ... ," he told a press conference.
He didn't confirm if the 40-year-old was known to the victim.
She was first to be notified when the arrest had happened.
"She [victim] is being supported by friends and friends
"We hope as an agency, she would feel a lot safer this afternoon than perhaps what she did this morning."
Mr Basham said the woman was recovering and would "take a while" to get over the ordeal.
Waitangirua has had "tough times" recently he said, with the police seige in a Kokiri Cres home, and this event had "potentially increased levels of anxiety" within the community.
"I'm confident and hopeful that after the swift arrest of the man, the determination shown by police and the fact that we have been able to put him before the courts, the community will take a great deal of confidence from that."
The man is set to appear in Porirua District Court tomorrow morning.
