The work will start Monday (9 February) and involves a lower speed limit and overnight lane closures. It is due to be completed, weather permitting, by the end of March.
Highways Agency project sponsor Dave Elwyn said:
The existing barrier has reached the end of its life and needs to be replaced to maintain safe and reliable journeys on this vital route. The work has been carefully planned and will be carried out overnight, when traffic flows are lowest, to minimise disruption.
There will be lane two closures overnight and a temporary 40mph speed limit in place throughout the work for safety reasons.
The work will take place between junctions 16 and 23 in both directions between 8pm and 6am.
Members of the public should contact the Highways Agency Information Line on 0300 123 5000.
Journalists should contact the Highways Agency press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.