The consortium of Balfour Beatty, Skanska, Atkins and Egis Road Operation UK is responsible for maintenance of the damaged section of the M1.
Work will start this weekend and be completed by Christmas.
The viaduct was badly damaged when fire broke out in a scrapyard beneath it in April.
Concrete repairs, parapet and bearing replacement, and new bridge joints are now needed to ensure the continued safety of the structure.
Paul Robinson, Highways Agency asset manager, said: “The work will be going on under the bridge, and we will be keeping traffic flowing on the M1 as far as possible.
“The nature of the work – hydro-demolition of concrete – means it will inevitably be noisy, but we will constantly monitor noise levels and take every measure possible to mitigate the effects on local residents.”
The southern span was the most badly damaged but remedial work is also needed to the northern span.