Formal identification would take place today, but police were confident the search for Millane had come to an end, AFP wrote.
"Based on the evidence we have gathered over the past few days we expect that this is Grace," Detective Inspector Scott Beard said.
"It is an unbearable time for the Millane family and our hearts go out to them."
A 26-year-old man was arrested on Saturday and charged with murder although no body had been found at that stage.
Beard said then that based on evidence uncovered during the investigation, they knew Grace was no longer alive.
Millane, 22, was last seen alive a week ago entering an inner-city hotel in Auckland with the man.
She 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.
Her father David, who reported her as missing, arrived in New Zealand on Friday and issued an emotional appeal for information relating to the disappearance of his "fun-loving, outgoing and family-orientated" daughter.
Police said there was no suggestion Millane previously knew the man she was seen entering the hotel with, but would not speculate on how they met.