The storms have caused flooding and road closures across areas of the country's east coast that have been ravaged by bushfires.
The start of the Australian Open tennis had been in doubt after smoke from the fires caused some players to suffer breathing problems.
That fear has now gone and the main tournament is due to start as usual on Monday.
Over a hundred fires are still raging despite the downpours.
Victoria, New South Wales and Queensland are having to deal with torrential rain in several areas.
Major highways have been closed and there have been power outages too in Queensland and new South Wales.
Voting ends in first phase of election in India's Bihar
Britain's Prince William calls for optimism on environment at EarthShot Prize event
Afghanistan and Pakistan return to Istanbul for more peace talks
Groping of Mexico's president puts violence against women in spotlight
Typhoon Kalmaegi death toll hits 114 in Philippines; heads to Vietnam
