David Millane, father of missing English backpacker Grace Millane speaks at a press conference in Auckland.
Speaking at the scene on Sunday afternoon, Det Insp Beard said investigators had "located a body which we believe to be Grace" around 10m from the roadside.
The last confirmed sighting of the 22-year-old was at 9.41pm the same day at the Citylife Hotel in central Auckland, when she was seen with a "male companion".
Formal identification would take place Monday, but police were confident the search for Millane had come to an end.
"This is a methodical and slow process and is expected to take all day".
She graduated from the University of Lincoln in England in September.
She had arrived in New Zealand on 20 November, following six weeks in South America.
The detective appealed for anyone who saw the vehicle in the west Auckland area between 6.30am and 9.30am on Monday to come forward.
Police said the man would be held in custody until his first court appearance on Monday. "It is an unbearable time for the Millane family and our hearts go out to them".
Mr Millane said his daughter had been "bombarding us with numerous photographs and messages of her adventures" before she went missing.
Ms Millane's father, David Millane, flew to Auckland and made a public appeal for help finding his daughter, who he described as a "lovely, outgoing, fun-loving (and) family-orientated".
Grace Millane, who was travelling the world after finishing university, went missing on December 1 in Auckland. Beard said she met a man for a couple of hours on the evening of December 1 before surveillance cameras showed them entering the CityLife hotel at about 9:40 p.m.
Last night, police announced that a 26-year-old man had been charged with her murder.
"We are all extremely upset, and it's very hard at this time to fully describe the range of emotions we are going through".