Work to mend the A591 and investigate restoring Pooley Bridge and Eamont Bridge is due to begin in the new year.
Cumbria County Council leader Stewart Young welcomed the money but said total restoration would cost much more.
"Repairing all the infrastructure in Cumbria alone will run into hundreds of millions of pounds," he said.
Transport Secretary Patrick McLoughlin said the local transport system was "the lifeblood" of the region.
"We are determined to help families and businesses in Cumbria and Lancashire get back on their feet as soon as possible," he said.
Engineers said severe flooding and landslides caused by Storm Desmond had left parts of the A591 looking "like a bomb site".
A £40m funding package for repairs to flood-damaged roads and bridges in Cumbria and Lancashire has been announced by the government.