Officers had earlier identified a countryside road on the outskirts of Auckland as a "location of interest".
A full examination, which started early this morning, remains underway in a bush area on Scenic Drive, in Waitakere.
A missing person search took a tragic turn on Saturday when investigators announced that they believed the 22-year-old, who was last seen alive on December 1, had been murdered.
Detective Inspector Scott Beard revealed the discovery of the body at a press conference near the search site about 4.30pm (local time) on Sunday. "A formal identification process will now take place, however, based on the evidence we have gathered over the past few days, we expect that this is Grace".
The British backpacker, who graduated from the University of Lincoln in September, had been travelling alone in New Zealand for two weeks.
Her father David, who reported his daughter as missing, arrived in New Zealand on Friday and issued an emotional appeal for information relating to the disappearance of his "fun-loving, outgoing and family-orientated" daughter.
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Police have appealed for sightings of the vehicle in the west Auckland area between 6.30am and 9.30am on Monday. "It is an unbearable time for the Millane family and our hearts go out to them", he told reporters near the scene.
On Saturday police released images of a pink watch and a necklace belonging to her and asked for the public's help in finding them.
"She arrived here on the 20th of November, and has been bombarding us with numerous photographs and messages of her adventures", Mr Millane said. Beard said she met a man for a couple of hours on the evening of December 1 before surveillance cameras showed them entering the CityLife hotel at about 9:40 p.m.
The man was with Ms Millane at several places, including Sky City, before going to CityLife Hotel with her.
She was staying at the Base Backpackers hostel in central Auckland before she went missing.
Her birthday was on Sunday, but she didn't contact her family.