The 26-year-old man has been speaking with police in Auckland in relation to her disappearance, officers said.
"Just after 3pm this afternoon, a 26-year-old man was located at a central Auckland address by police".
Ms Millane was last seen at CityLife Hotel in Auckland at 9:41pm on December 1, accompanied by the 26-year-old man.
'Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide.
"Grace's family has been advised of this development and they're devastated" Beard told the media.
"I want to reassure the public police are determined to do everything we can to find her".
Mr Beard said Ms Millane's passport, necklace and watch were still missing and police wanted anyone with information on these or anything else to get in touch on 0800 676 255.
Beard said police questioned the man seen with her that night and have named him as a person of interest - but he has not been taken into custody.
The revelation follows a forensic examination of a hotel where she was last seen on Saturday 1 December with a "male companion".
Ms Millane (pictured) arrived in New Zealand on November 20.
Ms Millane, from Essex, was described as a "lovely, outgoing, fun-loving, family-orientated daughter" by her father, David Millane.
The British backpacker, who graduated from the University of Lincoln in September, had been travelling alone in New Zealand for two weeks.
Asked if the pair had met on the Tinder dating app, the detective said: "I'm not going to speculate on how they met".
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
'Several of her belongings, including her passport, are missing and police believe it is likely Grace has these items with her'.
Searches have also been carried out at the backpackers' accommodation where she was staying.
Her father, David Millane, said they last had contact on the day she vanished.
Detectives have since assessed Grace's belongings, which were left at the backpackers where she was staying.
Earlier in the day police released photographs of a necklace and a watch in the hopes of finding her whereabouts.
The graduate's birthday was on Sunday but she did not contact her family.
"We are all extremely upset and it is very hard at this time to fully describe the range of emotions we are all going through".
"There's family back in the United Kingdom and our hearts go out to them as well".
Police said they had received dozens of calls to a hotline and more than 25 staff were working on the case, trawling through hours of CCTV footage to trace her movements.