The A66 will be closed overnight eastbound between 8pm and 6am, between the Greta Bridge junction and the Smallways junction, from Tuesday 25 August until Thursday 27 August.
Westbound traffic is unaffected at both junctions.
Highways England project manager, Chris Corcoran, said:
This vital resurfacing work will provide road users with a better driving experience. We will be carrying out white lining work which will improve driver safety, alongside other essential maintenance work during these closures.
We understand this work will cause some disruption for drivers and we would advise drivers to allow extra time for their journeys.
Eastbound traffic will be diverted at Rokeby Park towards Barnard Castle, along the A688 north for approximately 9 miles to the A68 at West Auckland and then towards the A1M at junction 58.
Members of the public should contact the Highways England customer contact centre on 0300 123 5000.
Journalists should contact the Highways England press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.