The approval, granted this week, represents the first major success for the new office. The scheme, when complete, will feature a new glazed pavilion, which will be a 'creative centre for the built environment'.
Backed by both CABE and Arts Council England, the project will also provide conference facilities.
The Orangery - which in the past 300 years has acted as a school, a bathhouse, a burial site and a zoological garden - is at the centre of a site set around the city's railway station that is earmarked for regeneration.
Also this week, SMC Alsop was shortlisted in the international competition for a 'Garden Ring City' in Singapore.