The Bureau of Meteorology says more rain is expected this afternoon, after some areas of the state received more than half their average rain for December overnight.
Senior forecaster Michael Laczko said the highest recorded totals overnight were at Cape Nelson with 44.8mm and Portland with 40.4mm.
Further east, Land Lang recorded 30mm and Wonthaggi, 25mm.
Mr Laczko said while there was a lull in the weather this morning, thunderstorms were likely to redevelop this afternoon and bring more rain around the state.
"We are expecting to see more heavy rain about the Otway Coast, Ballarat area and areas west of Melbourne, but all areas of the state are expecting showers and areas of rain to continue through the afternoon," he said.
Storms were likely to develop during the afternoon across Gippsland, the north east and north central areas, and could bring intense rain and localised flash flooding, he said.
A warning remains for sheep graziers in the north central, south west and central forecast districts, with cold temperatures, rain and showers and southwesterly winds are expected during the day.
Conditions would gradually ease later today, he said.
"We are expecting these conditions to gradually ease this evening from the west," he said.
"Areas in the west of the state will ease and clear earlier, and then overnight tonight conditions will ease significantly over the greater Melbourne area and ease early tomorrow morning about Gippsland and the eastern areas," he said.
"We're expecting a period of settled weather with just some isolated showers south of the Divide mainly tomorrow morning about the east of the state becoming clear and mostly fine for the next few days after that into Christmas."