Police have confirmed the body found at a rural property in Ardmore on Thursday afternoon is Rae Portman.
A post mortem that was carried out yesterday has officially identified her.
Detective Inspector Mark Gutry said it was very pleasing to give her family closure.
''Our thoughts are with Rae's family and friends. Having her back and putting her to rest means they can get on with grieving and having a bit of closure,'' he said.
An unexpected breakthrough
The breakthrough came when three police officers visited a rural South Auckland address - but they didn't expect to find a body.
The officers went to the Ardmore address to follow up the arrest of a 32-year-old Hamilton man accused of kidnapping Ms Portman. They became suspicious when they found items, including clothing, belonging to the missing 33-year-old.
They widened their search to a spot by some trees about 300m across a paddock and would only say the body was found "covered" - the Weekend Herald understands it was in an offal pit.
Investigators believe Ms Portman was killed about June 21 after she travelled to the Hamilton suburb of Te Rapa after visiting a Papakura address.
Detective Inspector Mark Gutry of Counties Manukau said the circumstances surrounding her death still needed to be established. But he confirmed police weren't acting on a tip when they visited the property, on Papakura-Clevedon Rd.
"When we went to the house we did not know we would be finding a body there ... We have arrested a man this week and as a result of the follow-up inquiries with that we came to this address."
Appeal for information
Mr Gutry said police were still seeking information from the public, especially movements of the yellow Holden Commodore ute with the licence plate LCKDUP and Ms Portman's black Mazda Astina.
"We believe those vehicles hold information about what happened to Rae and we're seeking information about their movements between June 20 and June 25."
The Mazda was found at a Hamilton wreckers' yard on June 25 but Mr Gutry would not say how it got there. "That's part of the investigation. We have identified the person who took it there but that's part of our inquiry."
The Hamilton man will reappear in court next month and has interim name suppression.
People with information about Ms Portman's disappearance are urged to call police on 0800 723 767, or anonymously through Crimestoppers on 0800 555 111.