The rule introduced by the former meant any council that didn't hold ceremonies on that date could be stripped of their right to hold citizenship events, as a number of Melbourne local governments refused to recognise the national holiday.
Councils can now hold the citizenship ceremonies any time from January 23 to 29.
Immigration Minister Andrew Giles said his government was "removing red tape" around the ceremonies, although he added it remained a "strong expectation" they were held on January 26.
"Australian citizenship is an important common bond for all Australians, whether by birth or by choice, and lies at the heart of a unified, cohesive and inclusive Australia," he said.
"The government's priority is to ensure that, where people have made the choice to become Australian citizens, they are afforded that opportunity in their own communities, with friends and family, in a timely way."
Mr Giles also announced the Yarra and Darebin City councils had regained authority to hold citizenship ceremonies, after former Prime Minister Malcolm Turnbull stripped them of that right in 2017.
Mr Turnbull described the councils as "out of step with Australian values".
A third Melbourne council - Merri-bek - announced earlier this month it would no longer hold events on January 26 and would instead host a mourning ceremony to acknowledge the experiences of Indigenous Australians.
"The very idea that we celebrate, hold parties and welcome new people to this country on this day is pretty shameful," Councillor James Conlan said at a council meeting on Wednesday night.
The federal government says there are less than 100,000 citizenship applications on-hand for the first time in five years.
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