Nadesalingam and Priya Murugappan fled Sri Lanka after the country's civil war, arriving separately on people-smuggling vessels in 2012 and 2013.
Home Affairs Minister Jim Chalmers said on Friday he had exercised his power under Section 195A of the Migration Act.
"The effect of my intervention enables the family to return to Biloela, where they can reside lawfully in the community on bridging visas while they work towards the resolution of their immigration status, in accordance with Australian law," he said in a statement.
"I have spoken to the family and wished them well for their return."
The couple met in Australia and married in 2014, and both were granted temporary visas settling in Biloela, where they had two daughters, Kopika, six and Tharunicaa, now four.
Nades worked at the local meatworks and Priya was a community volunteer.
In March 2018, immigration officers took the family from their Biloela home after Priya's bridging visa expired and Nades' refugee status claim was rejected.
They were taken to a detention centre in Melbourne.
This sparked a national campaign for the family to be allowed to stay in Australia and return to Biloela.
In late August 2019, the coalition government put the family on a plane bound for Sri Lanka.
But their deportation was sensationally halted mid-flight when a Federal Court judge granted a last-minute injunction.
The plane was forced to land in Darwin and the family was moved to the Christmas Island detention centre.
Facing pressure from community groups, lawyers, doctors and politicians, and with Tharunicaa needing medical care, then federal Immigration Minister Alex Hawke announced in June 2021 the family would live in suburban Perth under a community detention placement while legal action continued.
But he insisted the decision would not create a pathway to a visa.
In September, 12-month bridging visas were granted to Pria, Nades and Kopika, but not to Tharunicaa, which still meant the family could not return to Biloela.
Prime Minister Anthony Albanese said the cost to the family's health and the economic cost of their detention provided a clear reason to resolve the case.
"You can have strong borders without being weak on humanity," he said on Friday.
A friend and advocate for the family Bronwyn Dendle says the Biloela community was eagerly awaiting the decision, following Labor's announcement during the election campaign to help the family if elected to government.
"They've been watching the news just like everybody else to hear what's coming," Ms Dendle told Sky News on Friday.
"They would definitely be welcomed back with open arms and all of Biloela is just relieved that this has come to pass and that they (could be) allowed home.
"We are that town in central Queensland that stands up for their mates and leaves no one behind."