Officers had earlier identified a countryside road on the outskirts of Auckland as a "location of interest".
The body was found in a section of bushland off Scenic Drive in the Waitakere Ranges, about 30 kilometres southwest of Auckland.
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.
Millane, 22, was last seen at the Auckland city center the evening of December 1.
Police have said the examination is a "methodical and slow process and is expected to take all day".
He told reporters on Sunday: "A short time ago we located a body that we believe to be Grace".
Grace graduated from the University of Lincoln in September and had embarked on a year-long worldwide trip.
She arrived in New Zealand from Peru on 20 November.
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The detective appealed for anyone who saw the auto in the west Auckland area between 6.30am and 9.30am on Monday to come forward.
The man, whose name was withheld, is due in court on Monday morning. 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.
Millane had been in New Zealand for two weeks, the UK's Press Association news agency reported.
Saturday, police said they believed Millane was dead and that a man seen with her in Auckland the night she disappeared will be charged in her death. "We are determined to find her and return her to her family".
Before she vanished, Millane had been staying at a backpacker hostel in Auckland, and she left some of her belongings there.
Her family was surprised and anxious when she didn't contact them on her birthday or get in touch over on the days that followed.
Ms Millane, from Essex, was described as a "lovely, outgoing, fun-loving, family-orientated daughter" by her father, David Millane.
"We are all extremely upset, and it's very hard at this time to fully describe the range of emotions we are going through".