The 5km scheme has been dogged by delays since gaining planning permission in 2009 despite £37m of backing from East Sussex County Council.
A Hochtief/Vinci joint venture is in place to start construction.
Council Leader, Peter Jones, said “This is a once in a generation opportunity to make a step change to the most deprived local economy in the South East.
“There is overwhelming support for the road. It has planning permission and we resolved objections from the statutory environmental bodies, mitigating their environmental concerns.
“There were no environmental objections from any statutory body that were not overcome.
“Unlike other schemes, the link road is well advanced. It has planning permission, has been through a public inquiry process and there is a contractor ready to start work.
“Local businesses, the Local Enterprise Partnership and the local MPs all support the scheme.”