A contract notice for the £20m main works contract has been published and invitations to tender will be sent to selected companies in December.
Once construction gets under way, it is expected to take 21 months to complete.
The redevelopment of the Grade A listed building includes construction of a new copper-clad rooftop gallery extension and roof terraces and the construction of a new extension to the north of the existing building. The design (below) is by Gareth Hoskins Architects, which won the job in a national competition in 2009.
The council has agreed £10m towards the project and has underwritten a £10m public fundraising campaign. An application for the remaining £10m has been made to the Heritage Lottery Fund.
For more details, see our Contract Leads section.