Ms Millane, who turned 22 on Sunday, was last seen with a 'male companion'at CityLife Hotel, in Auckland, on December 1.
A 26-year-old man - who was with Miss Millane before she went missing - is being held in Auckland in connection with the murder.
"Sadly the evidence we have gathered to this point in the inquiry has established that this is a homicide. We are determined to find her and return her to her family".
Grace Millane, from Essex, graduated from university in September and had been in New Zealand for two weeks travelling alone.
Ms Millane (pictured) arrived in New Zealand on November 20.
Police said enquiries into Grace's disappearance have not led to further confirmed sightings of her.
"Grace's family have been advised of this development and they are devastated."
Millane, the daughter of English property developer David Millane, had not been seen since leaving her hostel in Auckland last Saturday.
Police had identified and found a vehicle of interest and officers were trying to find out where it had been, he said. He wouldn't give a description of the vehicle or say where it was found.
Police would like to hear from anyone who may have seen any of the items matching their descriptions over the past week.
Her other belongings had remained this week at Base Backpackers, where she had been booked in to stay until today.
Police said they were questioning a 26-year-old man about the suspected slaying of 22-year-old Grace Millane and a vehicle of interest had been secured.
But the detective added: "We still do not know where Grace is".
"We have no understanding of what the motive was". "We still don't know where Grace is". I'm not going to speculate on how they met.
"We still do no know where Grace is".
Beard said she met a man for a couple of hours on Saturday evening before surveillance cameras showed them entering the CityLife hotel at about 9:40 p.m.
Police have been conducting a scene examination at a unit in the hotel.
They had received several phone calls from the public and those were being "worked through and prioritised".
Despite a major police search and public campaign for information, no further sightings of the backpacker have been confirmed.
"Thank you to all who helped try and find Grace".
David Millane, the father of missing backpacker Grace Millane, says his daughter has "never been out of contact for this amount of time".
The Millane family are working with the Lucie Blackman Trust, which supports families of people in crisis overseas.
Detective Beard said Millane's case has been tough, at the press conference.
"Everyone who is a parent out there will understand and appreciate what the family is going through".
Police had been interviewing the unnamed 26-year-old about Millane's disappearance, and said Saturday that they would charge him with her murder.