She was last seen on the evening of Saturday 1 December.
Police said the body was in a forested area about 10 meters (33 feet) from the side of the road in the Waitakere Ranges near Auckland.
"Grace is a lovely, outgoing, fun-loving, family-oriented daughter", he said, adding that she was usually in touch with her family every day.
The body had not yet been formally identified, but it was believed to be that of Millane, Beard said.
Millane was on a year-long worldwide holiday after graduating from university and had kept in daily contact with her family until the night before her 22nd birthday last weekend.
"The focus now is to piece together exactly what happened to a young girl who came to New Zealand on her OE", he said.
"The evidence we have located so far, our scene examination, from the CCTV footage we have and our investigation has determined that Grace is no longer alive and this is a murder investigation".
Detective Inspector Scott Beard said during the conference officers had found the 26-year-old man at a central Auckland address at 3pm on Friday, and interviews were still taking place.
Grace Millane murder: New Zealand police search 'location of interest'
The man was with Ms Millane at several places, including Sky City, before going to CityLife Hotel with her.
Speaking from the scene, he said it was an unbearable time for her family and his heart goes out to them.
Police have appealed for sightings of the vehicle in the west Auckland area between 6.30am and 9.30am on Monday.
Police said the man would be held in custody until his first court appearance on Monday.
Police had "no reason or understanding what the motive was", he said.
On Saturday, a 26-year-old man was charged with murder in her case after he was detained for questioning.
Her family was surprised and anxious when she didn't contact them on her birthday or get in touch over on the days that followed.
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He also celebrate the success in a very ecstatic manner. "And whatever adjustments he had to make, he has already done it". The only difference is we get the covers off earlier and we start earlier.