1039 GMT November 22, 2019
The 22-year-old from Essex disappeared in Auckland on December 1, BBC wrote.
Police ended their search on Sunday after finding a body on the outskirts of the city.
Detective Inspector Scott Beard said the family was in "the process of organizing to take her home in the next few days."
A 26-year-old man has appeared in court in New Zealand charged with Millane's murder.
Millane's family said she "went off to travel the world in mid-October and arrived in New Zealand on November 20."
'Forever a Kiwi'
"By the amount of pictures and messages we received, she clearly loved this country, its people and the lifestyle," they said.
"We all hope that what has happened to Grace will not deter even one person from venturing out into the world and discovering their own overseas experience."
They called her death "heinous" but thanked police for completing a "concise, stringent and thorough investigation."
Millane's father David has flown to New Zealand and visited the place where her body was found.
He took part in a traditional Maori blessing ceremony alongside Grace's uncle and members of the New Zealand police force.
They added, "We would like to thank the people of New Zealand for their outpouring of love, numerous messages, tributes and compassion.
"Grace was not born here and only managed to stay a few weeks, but you have taken her to your hearts and in some small way she will forever be a Kiwi."
Millane had been traveling alone in New Zealand for two weeks, following a six-week group trip through South America.
Police believe she was killed between December 1 and December 2.
Bird said his team was building "a timeline of the circumstances."
"Work continues to piece together exactly what happened to Grace," he added.
Officers are looking for a shovel believed to be connected to the inquiry.