Britt Lapthorne's "broken" family will scatter flowers near where her body was found in Croatia, her grieving mother says.
Mr Lapthorne, his wife Elke and son Darren were extremely distressed on receiving the news about 5am (AEDT), they said in a statement released Saturday.
"They (the Lapthorne's) are extremely distressed and devastated by this news and ask that they be allowed privacy today," the family statement said.
"We're just broken people," Elke Lapthorne told Ten News tonight.
"I'm so proud of my daughter Britt and her courage, I'm so proud of my husband Dale and my son Darren."
Ms Lapthorne said Dale, who flew with 25-year-old Darren to Croatia to search for Britt, was "just shattered" at the news.
She said the family, sceptical of Croatian authorities, would also have a second autopsy carried out back in Australia.
"They will be scattering some flowers where Britt was found," she said.
"We will probably have another autopsy conducted here as well."
Ms Lapthorne spent the day in seclusion at the family's Melbourne home, supported by friends and family.
In Croatia, Mr Lapthorne and Darren did not feel able to talk to the media, closing themselves in their hotel room.
When Dale Lapthorne flew to Croatia to search for his missing daughter Britt, he vowed he would not return to Australia without her.
The Melbourne father will fulfill that pledge in the saddest of circumstances with news Saturday that DNA tests confirmed a body found off the coast of Dubrovnik is that of his 21-year-old daughter.
"Elke's extended family and friends are supporting her (Britt's mother) during this horrific time and she will be spending the day in the seclusion of her home."
Mr Lapthorne and his 25-year-old son are still in Dubrovnik, having travelled to the tourist town to find Britt.
Family spokeswoman Jacqueline Pascarl told AAP she believed Britt's father and brother would not return to Melbourne until they could bring Britt home.
"I believe that Dale and Darren have closed themselves into their hotel room and are trying to cope with this horrendous information," she said.
"I know that Darren and Dale will not return without Britt. I have no idea of the timeframe.
"Elke has spoken to me about Britt's love of life, her insight and empathy for others, her sense of humour.
"I hope she will be remembered as a young woman of 21 who was so much more than just the backpacker label ... as a beautiful daughter of a beautiful mother who is grieving tragically."
A spokesman for the hotel where Britt's father and brother were staying said Dale felt sick and was unable to address the press, Croatian news site Javno reported.
Overnight, Dubrovnik deputy police commander Ivan Kukrika told a press conference that DNA analysis had confirmed the identify of the body.
"DNA analysis has been completed in the capital, Zagreb," Kukrika said.
"According to the analysis, the body found in the sea on October 6th belongs to the missing Australian Britt Lapthorne."
Dubrovnik police crime squad chief Nikola Sakic said investigations were continuing into what happened to the Royal Melbourne Institute of Technology (RMIT) student.
Australian Foreign Affairs Minister Stephen Smith Saturday said he had rung Mrs Lapthorne, offering the government's condolences and assurance that consular officials would remain in Dubrovnik for as long as the family wanted their help.
"It is a terrible, terrible nightmare and we express our deepest sympathy to the family today," he told reporters in Newcastle.
"I spoke with Mrs Lapthorne this morning to personally express the sympathy and the condolences, not only on behalf of the government but on behalf of the Australian people.
"... And indicated to Mrs Lapthorne that we would ensure that our consular officials remained in Dubrovnik as long as Mr Lapthorne and his son want us to remain there, and we will assist in every possible way bringing them back to Australia and bringing Britt back to Australia."
The Lapthornes have experienced a roller-coaster ride of emotions since Ms Lapthorne went missing about three weeks ago.
She was last seen at a Dubrovnik nightclub in the early hours of September 18.
The family learnt through the Australian media that a body had been discovered on Monday in a bay not far from the town centre where Britt was last seen.
Croatian police had initially said the body - discovered by a local fisherman - was unlikely to be Britt because it was too badly decomposed.
Then Friday, a detective assigned to the case from Zagreb told the family media reports that the remains were those of a young, petite, blonde female were incorrect.
The family has critical of the Australian government, Australian Federal Police and Croatian police for what they said was lack of support and urgency.
Friday, Mrs Lapthorne's frustration was evident when she spoke to media.
"I'm losing hope. There are not highs anymore, only lows. It's a roller-coaster ride going down, down, down all the time," she said.
She said the Australian government was starting to take the case seriously, albeit too late, but she was still sceptical about Croatian authorities.
"I'm just hoping the authorities over there are not using Britt or this body and will identify it as Britt just so they can close the case over there. That's how it feels at the moment."
Saturday's family statement thanked the Australian public and media for their support.
"Dale and Elke, along with their son, Darren, wish to thank all Australians and particularly the media - who have provided such enormous support and determination in their efforts to assist in the search for Britt," it said.
Victorian Premier John Brumby said he hoped Saturday's news brought closure for the family.
"I can only extend my heartfelt sympathies to the Lapthorne family. I think they've shown extraordinary courage and it's unimaginable how difficult this is for the family," he said.