Investigation head Detective Inspector Mark Gutry said the body is believed to be Ms Portman's but results from a post-mortem examination will confirm that.
He said police were directed to the Ardmore address and found clothing and personal belongings of Ms Portman but Mr Gutry would not say what those items were.
A short time later they made the grisly discovery of the body, hidden at the rear of the property.
Mr Gutry said he could not go into details about what was found with the body.
He was also asked about the people who live at the property.
"We have spoken to them and we are satisfied they didn't know it was there.''
The family of Ms Portman has also been notified of the find.
"It is pleasing to give the family some closure and return the body to the family.''
Mr Gutry did not rule out further arrests in the case.
Police revealed last night that they had tracked Ms Portman's movements by tracing her cellphone activity.
Yesterday, a 32-year-old man appeared in court charged with kidnapping Ms Portman, who was four months' pregnant when she disappeared.
Detective Aaron Proctor told Police 10/7 Ms Portman left the motel about 9pm and headed south down the motorway in a black Mazda Astina to Markedo Place in Papakura.
"Her cellphone records show she was in this area just prior to 9.30pm on Wednesday, June 20.''
Her phone then began transmitting to a cellphone tower in Te Rapa, Hamilton, about 5.30am. "Our belief is she has travelled to Hamilton in that black Mazda Astina.''
Mr Gutry said today that police were still trying to piece together what happened to Ms Portman in Papakura.
"That's the information we need.''
Police believe a yellow ute - with the licence plate LCKDUP - travelled closely behind Ms Portman's car to Hamilton and they are seeking sightings of both cars from about June 20 and 21.
The car is today under secure lock and key at the Manukau police station.
Ms Portman's car was found in a Hamilton scrap yard on June 25. "We believe Rae has met her death in the Hamilton area ... What has happened to her in the Hamilton area on June 20, 21?'' Mr Proctor said.
The Hamilton man who appeared in the Papakura District Court yesterday charged with kidnapping Ms Portman could be seen wiping tears from his eyes as he looked at his mother in the public gallery.
Applications to take photographs and film the man were granted by the judge but an interim name suppression order was imposed after defence lawyer Shane Cassidy indicated he would appeal to the High Court against the decision.
Police opposed the suppression order because they believed publication of the defendant's name could assist the murder inquiry.
Police said more charges could follow.
The accused man will have until October 3 to lodge the appeal. He was remanded in custody until October 18.
