The project, between Barras and the border with County Durham, will provide smoother and safer journeys for road users.
The work will start on Sunday 9 March and should be completed by the end of the month, subject to weather conditions.
The carriageway will be kept open most of the time with lane closures for the resurfacing work. However, full closures of the eastbound carriageway will be needed overnight over two weekends. Long distance drivers will be advised to use the A69 trans-Pennine route from junction 43 of the M6 instead.
The four overnight closures will be taking place between 8pm and 6am on Saturday and Sunday March 15 and 16 and Saturday and Sunday March 22 and 23.
Highways Agency project sponsor Peter Gee said:
The carriageway surface along this section of the eastbound A66 is nearing the end of its serviceable life and needs to be replaced with new road markings too.
Over two weekends in March drivers using the A66 overnight as a through route into the North East will need to use the A69 instead and should leave extra time to complete journeys.