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The outbreak in Victoria's capital has seen hundreds of cases in the past two weeks - more than 95% of new Australian infections.
Until now, the two states had maintained open borders even when others had shut them.
The closure is to begin on Wednesday, Victoria's Premier Daniel Andrews said.
He said it had followed talks with Prime Minister Scott Morrison and NSW Premier Gladys Berejiklian, both of whom have previously said border closures weren't necessary.
"All of us agreed that the best thing to do is to close the border," Mr Andrews told reporters on Monday.
"This is one of those precautionary measures, it is one of those things that I think will help us in broader terms contain the spread of the virus."
Victoria's daily case increase
Source: Victoria State Government Natanz fire caused 'significant' damage |
Mr Andrews said those had "unavoidable travel" to NSW could apply for permits, including for people who had to cross state lines for work.
He acknowledged the border closure would most likely have a significant economic and social impact.
But it was necessary given "the significant challenges we face in containing this virus", Mr Andrews said.
Victoria reported 127 new cases on Monday - its highest daily increase since the pandemic began.
On the weekend, authorities enacted a "hard lockdown" on nine housing estate tower blocks - confining 3,000 people to their homes - after a cluster of cases were found.
Residents in at least 36 "hotspot" suburbs were put into a separate lockdown last week. Unlike those in the tower blocks, they can leave home for work, exercise, care and grocery shopping.
The outbreak has threatened Australia's relative success so far in suppressing the virus. Since January, Australia has recorded 105 deaths and around 8,500 cases. BBC