Rainfall of up to 100mm could fall in those areas by late tonight, Mr Corbett said.
The Otago Regional Council said rainfall was continuing to raise river levels in North and South Otago, and there was surface flooding in adjacent low-lying areas.
People were advised to watch out for surface flooding, slips, and hazardous driving conditions.
There were also road snowfall warnings around the Southern Alps, which received a heavy dusting of snow in places today.
There was also a "small chance'' of a tornado along the North Island's west coast, Mr Corbett said.
"These are not not like those big Wizard of Oz ones, these are more the smaller scale ... waterspout offshore.
"Hail, strong winds and heavy downpours are the main risk.''
"The southerly that's got the persistent rain to Otago and Canterbury, that whips up the country to Wellington tomorrow; it's one of those ugly days.''
Aucklanders could get an early morning wake up call, as thundery showers batter the city before dawn.
The worst will be over by sunrise, with lighter showers continuing throughout the day.
WeatherWatch.co.nz analyst Philip Duncan said by Wednesday the low pressure system would start to move out to the east.
"Meanwhile clearing skies push into parts of the South Island - with the sun returning.''
By the end of the week, the weather will have calmed, maybe bringing some cloud and fog patches as the wind dies down, he said.
@MetService Strange clouds over Aucklands North Shore this afternoon pic.twitter.com/yKqKr8VkOl
