Under the plans, the present building completed at the start of World War II, will effectively be rebuilt with the existing interior ripped out to leave only the building facade.
An extra storey would also be added, along with an atrium and a new council chamber.
The council has justified the scheme warning that it faces a bill of £14m to complete the maintenance backlog on the existing offices.
The newly-created council building will be more energy efficient and will see the building’s capacity rise from 500 to 1900 people.
Construction work is expected to start early next year and be completed by the end of 2012.
Under the proposals, the St Mary’s Gate and Roman House sites will be sold in 2013/14 to generate about £4.6m, while the rent paid for other council buildings will be reduced.