Work in the city centre will create a modern building less than a third of the size of the current County Hall building and will accommodate 1,000 staff.
Major works on site will begin in around four weeks and will see the building complete in autumn 2021.
As part of the project, Kier will create 250 new jobs in the local area that will be a mix of apprenticeships and employment opportunities for locals currently unemployed.
Tom Gilman, managing director for Kier Property North said: “We’re excited to be developing this 110,000 sq ft building and seeing the overall added value that this scheme will bring to the County.”
Brian McQuade, managing director for Kier Regional Building Scotland and North East added: “This project, in the heart of Durham City provides us with an excellent opportunity to not only deliver a first-class facility for Durham County Council but to also create exciting job opportunities in the local community.
“We aim to leave a positive legacy in all areas we operate and look forward to working with our local supply chain partners and Durham County Council to deliver this new project.”
Cllr Joy Allen, Cabinet member for transformation, culture and tourism at Durham County Council, said: “The development of the Aykley Heads site presents a once in a generation opportunity to transform the county’s economic prospects, with the development of what will be one of the most attractive business parks in the whole of the North East, and has the full support of the business community.
“The planned development will create thousands of new high-quality jobs and future employment opportunities for our young people, as well as bringing millions of pounds of investment into the county.”
Following the opening of the new headquarters, the current site of Durham County Hall at Aykley Heads has been earmarked as the site for a new multi-million-pound business district that could create 6,000 new jobs and deliver a £400m boost to the county economy once complete.