With road and rail links still cut, the Commonwealth and SA governments will jointly fund repairs to key public infrastructure through disaster recovery arrangements.
The initial assistance will ensure councils can cover the costs associated with clean-up activities, restoring roads and keeping communities safe.
Emergency Management and National Recovery Minister Bridget McKenzie said the heavy rain and flooding had caused major problems for local residents as well as disrupting supply chains.
She said the government had already provided assistance with the delivery of food and supplies to those affected by road and rail disruptions.
"We continue to stand side by side with South Australians who have been impacted by this severe weather event," Senator McKenzie said.
"We are ready to provide additional assistance measures once further recovery needs assessments have been undertaken."
Premier Steven Marshall said everything was being done to repair infrastructure damage as quickly as possible and make sure there was food and medical security for cut-off communities.
"No stone has been left unturned in our efforts to help our regional communities who have been dealt a fierce blow with many extreme weather fronts over the last few weeks," he said.
"A significant logistical and coordinated multi-agency response has been required to make sure affected communities have been looked after."
Among the communities to be provided with assistance are those in the state's north, on Eyre Peninsula and on the state's west coast.
During the rain and floods last month, the State Emergency Service received more than 800 calls for assistance.
The outback drenching made the Stuart Highway, the main road link between Adelaide and Darwin, impassable.
Freight started to flow through the flooded section on Monday but it could be until next week before the highway is open to all traffic.
The Australian Rail Track Corporation said the trans-Australian railway was expected to reopen on February 15 after repairs to 18 sections of track across 300 kilometres of line.
"ARTC will now work with our customers to ensure operations can commence safely and that freight can get moving on this vital rail link connecting Western Australia and the Northern Territory," a spokesman said on Tuesday.
The Bureau of Meteorology said the rain over central Australia in January was brought by former tropical cyclone Tiffany as it moved south.
As a result, falls across the state last month were 175 per cent above average with SA recording its fourth-wettest January on record and its wettest since 1984.
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