The Lee family have lived in Australia for nine years and were due to be deported to South Korea next month.
“I cried when I heard the news, the tears are still left in my eyes... I’m so very, very happy,” the father David Lee told SBS World News.
The family who had moved to Australia in 2008 had been a victim of a scam losing $100,000 to a migration agent who later fled the country.
The family had also received bad legal advice from a lawyer assisting them with their claim.
Their ordeal prompted a campaign from the local community, who set up a petition calling for them to be allowed to stay.
They also received support from their local Catholic community, with the Catholic Archbishop of Melbourne Denis Hart lobbying the government on their behalf.

Mother Jessica Lee was is disbelief when she was told they had been granted a permanent visa. Source: SBS News
Their local MP Julian Hill met with the family and agreed to lobby Assistant Immigration Minister Alex Hawke.
The mother Jessica Lee said she couldn't believe the ordeal was finally over, and the family had been granted a permanent visa.
Twenty-one-year-old Brian Lee said the outpouring of community support has been heartening.
“In this whole process we had a lot of people supporting us and a lot of people helping us, that was enough to bring happiness on its own,” he said.
He said the certainty around the decision means he is now able to plan his life and university studies.
“Now I can plan ahead of time without fear of having to leave at any moment, it is really great having that uncertainty going away,” Brian said.
The family’s local priest Father Pat Jackson from St Christopher’s Church said the last minute reprieve was a miracle.

23 year old David Lee says he will now be able to complete his university studies. Source: SBS News
“It was action and prayer both going together... [the campaign] just felt elated and lifted by the support of the Catholic and Korean community,” Mr Jackson said.