Detective Inspector Scott Beard said just after 3pm a 26-year-old man was found at an address and is speaking to police about the murder of Grace Millane.
Officers searching for 22-year-old Grace Millane are now "conducting a scene examination" at an apartment in the Citylife Hotel, Queen Street, Auckland.
New Zealand Police said the man will remain in custody until Monday morning, when he will appear in the Auckland District Court.
'Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide.
"Grace's family have been advised of this development and they are devastated".
The 22-year-old, from Essex, described by her father as "lovely" and "family-orientated", vanished in New Zealand a week ago.
A 26-year-old man is being held in connection with her murder and a vehicle of interest has been found.
She was last seen in Auckland on December 1.
After visiting Peru she arrived in New Zealand on November 20 and had been near-daily contact with her family until December 1.
Grace Millane's belongings, including a necklace and a Baby-G watch.
Beard said Millane had been out of contact with her parents for days and, especially worrying to her family, they weren't able to contact her on Sunday for her 22nd birthday.
Despite a major police search and public campaign for information, no further sightings of the backpacker have been confirmed.
Millane graduated from the University of Lincoln in September before beginning her trip.
Asked if they had met on the Tinder dating app, the detective said: "I'm not going to speculate on how they met".
DI Beard said the investigation into Grace's disappearance was "progressing rapidly".
Detectives have since assessed Grace's belongings, which were left at the backpackers where she was staying.
They revealed yesterday that their investigations included questioning the man who was with Millane when she was last seen.
Earlier searches of Ms Millane's accommodation at a backpackers' hostel found several items, including her passport, were missing.
Police released images of Ms Millane's watch and necklace earlier on Saturday. He also said investigators were looking into her credit card activity to see the last time she made a transaction.
He said police were working on reviewing hours of surveillance camera footage from around the city, which has proved crucial in tracking Millane's movements.
"We've spoken to David [Grace's father] we've met him, but there is family in the United Kingdom and our hearts go out to them as well".
"As a family we have been extremely concerned for her welfare", he said.