The Murugappan family - dubbed the Biloela family - will be released into the community after intervention from Labor, ending more than four years in detention.
But the new government says it is not abandoning its hardline border stance by ending years of limbo for the family, insisting future boat arrivals will be turned back.
The former government had attempted to deport the four despite objections from the community of Biloela, the central Queensland town they had made their home.
Parents Priya and Nades, and Australian-born daughters Kopika and Tharnicaa - dubbed "anchor babies" by likely opposition leader Peter Dutton in 2019 - will now be able to return to the central Queensland town of Biloela, where they lived before their detention.
Priya said in a message via friend Angela Fredericks: "Finally, everything is here. I cannot believe it. My prayer is that this government will make a change to the lives of every single refugee who comes here.
"All refugees are survivors. They need hope".
Ms Fredericks said Priya and Nades had shared their "overwhelming sense of joy and relief" when told of the news.
"We all welcome the decision to issue the entire family with bridging visas. But this family will never be safe until they have permanency in Australia," she said.
The family anticipates leaving Perth in early June.
Interim Home Affairs Minister Jim Chalmers on Friday revealed he had used ministerial authority to ensure the family, which the former government had attempted to deport, could "reside lawfully" in their adopted home.
"I have spoken to the family and wished them well for their return," he said in a statement.
"This decision will allow them to get 'home to Bilo', a big-hearted and welcoming Queensland town that has embraced this beautiful family.
"This government remains committed to Operation Sovereign Borders and keeping people smugglers out of business."
Dr Chalmers stressed Labor remained committed to returning boats seeking to enter Australian waters to their point of origin.
Sri Lankans Priya and Nades both arrived in Australia via boats arranged by people smugglers in 2012, before marrying and settling in Biloela, where they were highly-popular. Nades worked at the local meatworks and Priya was a community volunteer.
They were detained in 2018 and courts found they were not refugees, a decision subsequently upheld.
But a 2019 attempt to deport the four was halted at the 11th hour, when a court injunction forced the plane carrying them to land in Darwin.
A federal court then ruled the youngest daughter Tharnicaa, now four, should remain in Australia along with her family as her claims to a protection visa were assessed. The family was taken to Christmas Island detention.
The family's long-term future hinged on the outcome of Saturday's election, with Labor pledging to release them if it won government.
The Coalition last year removed the four from detention on Christmas Island, but only into community detention in Perth as the legal process played out.
The former government had claimed releasing the Sri Lankan parents Priya and Nades, who worked in Biloela and grew roots in the community, would revive the people smuggling trade.
Peter Dutton, all but certain to become Liberal leader on Monday, described their Australian-born daughters as "anchor babies" - widely viewed as a pejorative - in 2019.
"It's been very clear to them at every turn that they were not going to stay in Australia, and they still had children," he said.
"We see that overseas in other countries, anchor babies ... the emotion of trying to leverage a migration outcome based on the children."
Tharnicaa was rushed to hospital last year fighting a blood infection, more than a week after supporters said her condition began to deteriorate.
Friday's decision ends more than a year of political division over the family.
In opposition, Labor demanded then-immigration minister Alex Hawke use his ministerial discretion to grant the family a release.
Their fate also created internal division within the Coalition, with former deputy prime minister Barnaby Joyce suggesting the two girls would be treated differently "if their names were Jane and Sally".
Former cabinet minister Angus Taylor said the High Court had found the Murugappans weren't refugees and the Labor government's decision sent the wrong signal to people smugglers.
"I totally understand the compassion people feel towards the family, but it's important to have compassion towards the 1200 people who died at sea on those 800 boats when Labor was last in power, when the wrong signal was sent to people smugglers," he told Sky News.
"If people can come in who don't have refugee status, then you know, it's a major issue to then allow them to come into Australia."
- with AAP