Millane had been travelling after finishing her studies at university.
Detectives charged a 26-year-old man with her murder yesterday but had discovered no body until their investigation led them to a "location of interest" today.
A man, 26, was charged with murder Saturday after he was last seen entering the CityLife hotel in Auckland with Millane, who had arrived in New Zealand on November 20 as part of her yearlong backpacking trip across the world.
The man accused of murdering British backpacker Grace Millane made his first appearance this morning in the Auckland District Court.
"All of us hope justice for Grace is fair and swift, and ultimately brings you some peace".
"It is an unbearable time for the Millane family and our hearts go out to them", he said.
In a statement released by her family earlier this week, Millane was described as "a fun loving, outgoing and family-orientated person". Beard said she met a man for a couple of hours on the evening of Dec 1 before surveillance cameras showed them entering the CityLife hotel at about 9.40pm. "The focus now is to piece together exactly what happened to a young girl who came to New Zealand".
"These kinds of things don't help the situation but as I say I think these are reasonably isolated incidents towards tourists and from that perspective, we don't see it having an impact long-term as long as it is isolated".
Police want to trace the movements of the car
Police have released two photographs of a 2016 red Toyota Corolla hatchback was hired from a central Auckland rental auto company just before lunchtime on Sunday.
Grace graduated from the University of Lincoln in September and had embarked on a year-long worldwide trip.
He added that Millane's family had been informed.
She had arrived in New Zealand on 20 November, following six weeks in South America.
Grace's body was found about 10 metres from the side of the road, hidden in bushland, and is believed to have been taken there in a rental vehicle that was recently found almost 300 kilometres (186 miles) away in Taupo.
However, police said several of her possessions, including her passport, are missing.
Millane was last seen with a "male companion" on December 1, a day before her birthday.
Detective Inspector Scott Beard told reporters late on Saturday that the man, who was not identified by name, has been charged with Millane's murder.
She had booked to stay at the Base Backpackers hostel in central Auckland until 8 December.