The 5km dual carriageway will run between Newton Abbot and Torquay, bypassing the village of Kingskerswell.
The majority of the scheme is funded by the Department of Transport with significant additional support from Devon County Council and Torbay Council.
Detailed design work is due to begin this month with construction to complete by the end of 2015.
Greg Fitzgerald, chief executive of Galliford Try, said:
"We are delighted to be awarded this major and prestigious contract which will result in significant economic and environmental benefits and also improve safety.
“The link road is a great opportunity for us to further strengthen our presence in the south-west, a region where we are well established as a housebuilder."