In the past fortnight, New South Wales (NSW) and Queensland have been pummelled by heavy downpours that have caused floods and killed 20 people, BBC reported.
The threat has now intensified in Sydney, which has been hit by widespread flash-flooding.
Two bodies - believed to be of a woman, 67, and her son, 34 - were found in a Sydney canal on Tuesday.
Police said their deaths would be investigated, but noted the canal had risen "from ankle-deep to above neck height in a matter of minutes".
NSW Premier Dominic Perrottet said 40,000 residents in the state had been ordered to evacuate, and another 20,000 people were on standby.
He added that a dam in the suburb of Manly had begun to spill, and a flooded river was threatening lives in the city's southwest.
There was also a "substantial catastrophe" in the state's north, where more than 800 people had been placed in temporary accommodation.
The State Emergency Service said more than 2,500 people had requested help in the past 24 hours. Australian Defence Force soldiers have also been deployed.
Experts say the flooding emergency has been worsened by climate change and a La Niña weather phenomenon. A La Niña develops when strong winds blow the warm surface waters of the Pacific away from South America and towards Indonesia. In their place, colder waters come up to the surface.
In Australia, a La Niña increases the likelihood of rain, cyclones and cooler daytime temperatures.
MP/PR