South Australian Premier Peter Malinauskas has warned residents to prepare for the risk of flooding in the days ahead.
The state's southeast - which has barely had a drop of rain all year - could get local falls of up to 100 millimetres, with accumulations of up to 40mm in an hour.
Mr Malinauskas said the weather system's unpredictable nature meant the whole state was on alert.
"It is not unusual in South Australia or metropolitan Adelaide to see a 10-millimetre rain event," he said.
"But when we start to see rain events north of 50, 60, 80ml, that starts to represent the sort of conditions where we will see flash flooding.
"If we see that volume of rain in a short period of time, then we should anticipate flash-flooding events throughout the state."
Mr Malinauskas said while the rain was poorly timed for the state's famed viticulture industry, it would also bring relief to many.
"For pastoralists and the grain-growing community, much of this rain will be very welcome indeed," he said.
Jon Fischer, a senior meteorologist at the Bureau of Meteorology, said the slow-moving nature of the tropical low - which had sat over the Simpson Desert in the southeast Northern Territory for a week - was highly unusual.
"We've all seen images of roads being washed away, impacts to the rail line and usually dry creeks turning into torrents," Mr Fischer said.
The system is forecast to move southeast over the course of the weekend, with a flood watch issued for all catchments across the state.
Adelaide was expected to feel the effects late on Sunday and overnight into Monday morning.
A severe weather warning was already in place for the South Australia's west coast, west pastoral and Eyre Peninsula districts.
By next week, the system was expected to push into western Victoria, with falls of up to 150mm anticipated.
Flood warnings remain in place for large parts of central Australia, with much of the water flowing into Kati Thanda-Lake Eyre.
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