The road will ease congestion in the North West, taking traffic driving from Morecambe and Heysham away from Lancaster city centre.
The DfT has pledged the vast majority - £133M of the project costs, Lancaster council providing the remainder.
Transport minister Paul Clark said: "This scheme will significantly improve links for freight traffic between Heysham Port and the M6 and will also mean that all traffic travelling between the M6 and the Morecambe and Heysham peninsula will no longer have to journey through Lancaster city centre.
"This will bring much-needed congestion relief to Lancaster's historic centre, improve road safety and the local environment, as well as providing an opportunity to introduce better public transport.
"The Government is committed to investing in transport links, particularly when they help boost economic growth and regeneration. That's why I am pleased to announce £133M Government funding for the completion of the Heysham to M6 Link. "
The new 4.8km dual 2-lane carriageway will bypass the north of Lancaster and connect the A683 to junction 34 of the M6 motorway near Halton. 24 new structures, including new bridges crossing the West Cost Mainline, Lancaster Canal and the River Lune. A combined footway/cycleway will run along the full length of the road.
The funding package also includes a new design for junction 34 of the M6 with improved safety standards for the slip roads.
Phase 1 of the Heysham to M6 Link was completed in 1994, removing traffic from residential areas in Morecambe and Heysham but most of this traffic still travels through the centre of Lancaster to reach the motorway network.