Local contractor R G Carter is currently on site working on the first of three phases which were originally budgeted at £22m.
Further surveys of the 1960s building have now revealed the cost of the work will rise to £32m.
Extra work will focus on energy efficiency, waterproofing roofs, structural repairs to the concrete frame and improved fire prevention measures.
Nearly 3,000 council staff will eventually work from the revamped building.
Steve Morphew, Cabinet Member for Finance, Corporate and Personnel, said: “This is a major ‘spend to save’ scheme started by the last administration and we have brought forward the work programme to realise savings sooner.
“In domestic terms this is like fitting a new boiler – there’s an initial outlay that you expect to recoup in lower fuel bills, but we are doing it on a much larger scale.
“It is a big scheme that will reduce the number of buildings we pay for, reduce fuel bills and enable the council to work a lot more efficiently.
“These will not be plush or luxurious offices but they will be modern and able to meet the needs of Norfolk in a better and cheaper way for the next two decades.”