Kier will start on site this spring to restore the Grade II listed Mount Oswald Manor House and turn it into a local history hub, bringing together archive, heritage, and registration services at a single location.
Construction is expected to be complete by next autumn.
Construction information specialist BarbourABI valued the contract at £14m and said Kier fought off competition from Galliford Try and Wates to win the deal for Durham County Council.
Council leader Simon Henig said: “We are delighted that a main contractor has been appointed so that work can begin on the exciting new centre which will provide a unique gateway to explore the whole history of the county and its people.
“It will allow us to open up new spaces for residents and visitors to use and enjoy as well as providing a secure future for our important heritage collections.”
Dan Doherty, regional director at Kier Regional Building North & Scotland, said: “We have vast experience in restoring first-class refurbishments of Grade Listed properties and look forward to being part of this iconic scheme for County Durham.”