The new 4.7 mile dual carriageway will run between Junction 19 of the M6 near Knutsford and Junction 7 of the M56 near Bowdon.
It will take traffic away from local villages, by-passing Over Tabley, Mere and Bucklow Hill.
The new route will run to the west of the existing A556 and will be built below ground level where possible to minimise the impact on the surrounding area.
The road will rejoin the existing A556 for a short section near Bucklow Hill, which will be upgraded.
Improvements will also be made to the layout of Junction 7 of the M56.
The road improvement scheme has been granted development consent by the Planning Inspectorate.
