The county council, Costain and Jacobs have worked together to submit the three-mile dual carriageway plan, which runs from the A589 to junction 34 of the M6.
During the next six months, the Infrastructure Planning Committee will scruntinise the plan, which includes a new bridge over the River Lune, before making a recommendation to the transport secretary who will decide whether to approve it.
If it gets the go-ahead the hope is to start construction during the summer of 2013.
Andrew Langley, Costain Project Manager said: “This is a major achievement for the whole Heysham to M6 Link team as the approval process is extremely rigorous and it’s no surprise that there have only been 13 applications to the IPC in nearly 18 months.
“We have proved the advantages of a totally integrated team approach to delivery of an application on this major highway scheme,” he added.
The IPC is due to become part of the Planning Inspectorate in April 2012 but all applications with respect to nationally strategic or major infrastructure projects will remain unchanged.