A team including BDP and Taylor Woodrow has been chosen to design and construct the four-storey building.
It will be 330 ft (100 m) long and 30 ft (9 m) wide, and occupy a linear site running between the Royal Festival Hall and Hungerford Railway Bridge, extending into the viaduct's arches.
The building will provide office accommodation for Royal Festival Hall staff, freeing up much needed space in the main building for expanding cultural activities.
Retail space will be accommodated in mezzanines constructed within the railway arches and on the second floor of the building, which fronts onto Hungerford Terrace.
The project will start on site this summer, and is expected to be completed in time for Christmas next year.