Stockport Council awarded the deal through the Highways England CDF Lot 2 Framework to design and construct the new Travis Brow Link Road between the A6 and M60.
The route is part of the council’s £73m Town Centre Access Plan to ease congestion in Stockport.
Graham will now work with Mott McDonald to complete the works in partnership with local contractor George Cox & Sons.
The new road will carry traffic under the Stockport Viaduct which dates back to the 1840s.
The contract also includes improvement works to the A6 Wellington Road North, the A5145 Travis Brow and the adjacent George’s Road.
Construction is anticipated to be completed in August 2018.
Leo Martin, Executive Director at Graham, said: “This link road development forms a key part of an extensive access plan for Stockport town centre, with high-levels of expertise required in order to complete the work – especially when you take into consideration the Grade II listed viaduct and tunnel.
“Our team is well-prepared and adapts to all working landscapes to ensure that all of our projects are completed on time and to a high standard.