The 5.7km Congleton link road scheme aims to unlock the potential for new homes and create 3,400 jobs.
In addition, it will boost connectivity to other major towns and the motorway network as well as improving road connections to Congleton Business Park and Radnor Park Trading Estate.
The route will link the A534 Sandbach Road, near its junction with Sandy Lane, to the A536 Macclesfield Road, near its junction with Moss Lane and provide a new village crossing at the river Dane.
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The project will be half funded by the government and £23m will be provided by developers. The council will meet the remaining £22m cost.
Following approval, the scheme be referred to the Secretary of State for communities and local government for a final decision on the planning application.
Cllr David Brown said: "I am pleased that both Cabinet and the strategic planning board have reached these decisions.
"This is the biggest road infrastructure scheme undertaken by this Council and I know it will be of enormous relief to many people in Congleton to know that it is proceeding.
"The link road will relieve traffic congestion in Congleton and, as a result, will boost the local economy by opening up new sites for development and create new opportunities for businesses and workers."
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