The partners also plan to extensively refurbish the 309,000 sq ft existing shopping centre at Canada Water on Rotherhithe Peninsula under the £30m investment plan.
Construction work is due to start on site in spring 2013 with completion scheduled for summer 2014.
Up to £4m will be invested in public realm improvements around the centre as well as improved connections to Surrey Quays station and Canada Water tube and bus stations.
David Pollock, retail development manager for British Land, said: “The approval for the Surrey Quays Shopping Centre extension is important for the wider regeneration of Canada Water and Rotherhithe and demonstrates our commitment to the area.
“The extension and refurbishment will create additional space that will allow us to attract and accommodate new and exciting retailers, ensuring that Surrey Quays remains competitive in today’s market.
“The current shopping experience will be significantly improved for both existing and new customers.”