Millane had been travelling after finishing her studies at university.
On Saturday, a 26-year-old man was charged with murder in her case after he was detained for questioning.
Grace Millane went missing on December 1 in Auckland, New Zealand's most populous city, just one day before her 22nd birthday. His name has been withheld, and he is due in court on Monday.
A full scene examination is now underway at a bush area on Scenic Drive, Waitakere Ranges in West Auckland.
Formal identification would take place Monday, but police were confident the search for Millane had come to an end.
Judge Thomas acknowledged the Millane family, who were present in court, and said he recognised the huge grief they must be feeling.
He added that Millane's family, including her father who has flown to New Zealand on Friday, has been informed. "Any father, any parent in this situation would struggle".
He said Kiwis are shocked and horrified when something like this happens which shows that New Zealand is a safe country.
The family of a British backpacker whose body was discovered in New Zealand has paid loving tribute to her memory, as her brother shares poignant photographs with the message: "You are my sunshine, my only sunshine".
By 4pm they had found her body.
Millane was on a year-long OE after graduating from the University of Lincoln in September.
Police have reached out to the public with a request for information about the case and released a photograph of the rental auto connected with Millane's murder investigation.
This was her first time travelling overseas alone.
The last confirmed sighting of Ms Millane was at 9.41pm the same day in her hotel, when she was seen with a "male companion".
Police have released two photographs of a 2016 red Toyota Corolla hatchback was hired from a central Auckland rental vehicle company just before lunchtime on Sunday.
According to the BBC, Millane had been in New Zealand for around two weeks after finishing up a six-week group trip to South America.
- December 5: Millane is reported missing to City of Auckland Police.
Police haven't said if those items were found with her body.
Police said there was no suggestion Ms Millane previously knew the man she was seen entering the hotel with, but would not speculate on how they met.
She had booked to stay at the Base Backpackers hostel in central Auckland until 8 December. The man was not taken into custody and police said there was no evidence of foul play.