The firm is understood to have fended off rival bids from Kier, Lagan and VolkerFitzpatrick with a final price of £19.8m.
Graham will now build a new 400m long multi-span viaduct and approach embankments. It will be constructed of “weathering steel” beams with a concrete deck on elliptical columns.
Once complete the 16m wide viaduct carrying the 3-lane A138 carriageway over the River Chelmer will be demolished.
The new 17-span structure will take around two years to complete and will be built to the east of the existing viaduct and connect into the Army and Navy and Chelmer Village Way Roundabouts at either end.