The £10.4m offices in Botchergate will allow the council to cut its office buildings in the city from 22 to just two by 2018.
It currently faces a £13m maintenance backlog liability on existing accommodation, along with high running costs. Selling the majority of these offices and moving to a custom-built premises will save around £1m each year.
Council Leader Stewart Young said: “The council has to make the best out of the financial situation it is in.
“Our downsizing deal is a crucial part of making the organisation ready to face the future. We need modern, flexible accommodation with lower overheads.”
John Wilson, Managing Director of Eric Wright Construction, said: “Working in partnership with our design team of AHR Architects, Hannan Associates and Curtins Consulting, we’ve extensive experience in creating high-profile, bespoke office accommodation for clients across the UK and we believe we are the right team to deliver such a project that will help Cumbria County Council achieve its commitments to ongoing overhead reductions and cost savings.”