Her dad David flew to Auckland from the family’s home in Essex after Grace, 22, was reported missing while staying at a backpackers’ hostel in the North Island city earlier this month.
Her body was found in bushes 30 feet from the road in the Waitakere Ranges, just outside the city, on Sunday after last being seen on December 1.
Today David issued a statement saying: "After the disappearance of Grace on 1st December 2018 our whole world turned upside down.
"Gill, Michael, Declan and myself would sincerely like to thank everybody involved and express our most profound gratitude.
"In this difficult situation where everybody is a true hero it is sometimes difficult to single out certain people."
Grace's body was found near Scenic Drive, a winding road that cuts through the eastern fringe of the forest. A 26-year-old man has been charged with her murder.
David added: "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 OE.
"Martin and I had the privilege of attending the traditional Maori blessing of the site which was a lovely and peaceful experience.
"Finally 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.
"My brother Martin and I leave for the UK this weekend to take her home."
Before Grace's body was found, David made an emotional appeal for help, describing her as a "lovely, outgoing, fun-loving, family-orientated daughter".
Her alleged killer, who cannot legally be named, has been charged with Grace's murder and appeared in an Auckland court on Monday.
Detective Inspector Scott Beard revealed Grace’s body was found “intact” in an area of bush by Scenic Drive, which runs through the hills.
He said officers are now hunting for an Atlas Trade hardwood long handle, round mouth shovel and appealed for anyone who may have found it after December 3 to come forward.
“At this point we don't know where this item is,” said Mr Beard.
“It could be anywhere between the Scenic Drive and central Auckland areas.
"Someone may have come across it, picked it up and taken it home. We need to speak to that person or anyone who has seen it."
Officers said they have received "hundreds" of calls about the case and investigators are trying to establish a timeline of events.
They said a “location of interest" was identified after the investigation led them to a spot on Scenic Drive.
The last confirmed sighting of the University of Lincoln graduate Grace was at 9.41pm on December 1, the day before her birthday, at the Citylife Hotel, when she was seen with a "male companion".
Since arriving in New Zealand from Peru on November 20, she had been in near-daily contact with her family in Essex.
Police received a missing person report Wednesday 5, and began a major search as well as a public campaign that saw dozens of calls made to a helpline.
David flew to Auckland and made a public appeal for help finding his daughter, who he described as "lovely, outgoing, fun-loving (and) family-orientated".
Her brother, Declan Millane, paid tribute by sharing pictures on social media of him and his sister, adding the lyrics of You Are My Sunshine.
He wrote on Instagram: "You are my sunshine, my only sunshine. You make me happy when skies are gray. You'll never know, dear, how much I love you. Please don't take my sunshine away.
New Zealand's prime minister Jacinda Ardern gave an emotional apology to Grace's family, saying: "Your daughter should have been safe here, and she wasn't, and I'm sorry for that. I cannot imagine the grief of her family and what they would be experiencing and feeling right now."
A GoFundMe campaign has now been set up in Grace's memory.
Funds raised will be given to Lincolnshire-based cancer charity Candles and the Lucie Blackman trust, who help British crime victims overseas and have supported Grace's family during this time.
It has emerged the man accused of the murder was due to go on a Tinder date on the night Grace was murder but cancelled it.
He is reported to have dated a number of Brit backpackers and liked “the admiration of young females”.
Criminologist Greg Newbold said the suspect, who has not applied for bail, is likely to be the target violence in prison.
"At the moment he'll be public enemy number one … but you have to remember he hasn't been tried yet."
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