Scott Morrison said the babies and their families would not be sent back to the government detention centre on the Pacific island of Nauru while their refugee claims are assessed.
"Along with those 31 babies, I am also allowing their immediate family members to have their protection claims assessed in Australia," Morrison said in a statement.
"This includes their mothers, fathers and siblings. That is, around 80 family members, all of whom are already in Australia having been transferred from Nauru, for the birth of their child."
Morrison's comments came just before a federal court rejected an appeal against a decision in October to deny Australian-born baby Ferouz refugee status even though he was delivered in Brisbane's Mater Hospital last year.
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Ferouz, whose mother is from Myanmar's persecuted Rohingya minority, is one of the babies that will benefit from the decision.
His lawyers from Maurice Blackburn welcomed the announcement and described it as a "positive step forward".
"Importantly, these babies and their families have only cleared the first hurdle. They still need to have their applications for refugee status considered," a spokeswoman for the law firm said.
Canberra has adopted a hardline stance against asylum-seekers who arrive in Australia by boat. Since July 2013, they have been denied resettlement in the country and sent to camps in Nauru and Papua New Guinea.
Morrison warned that the asylum-seekers would only be eligible for temporary visas and those currently held in one of Australia's offshore processing facilities "must not think this decision gives them a ticket to Australia".
"It does not. They will remain and be processed at the (regional processing centre). The Government's strong policies of turning back illegal boats, offshore processing and temporary protection visas remain in full effect," he said.