A refurbishment of the existing 29,000 sq m shopping centre is also proposed.
The centre is owned by Surrey Quays Ltd, a joint venture of British Land and Tesco.
The extension will sit in front of the existing entrances to the shopping centre and provide 18 new shops and restaurants plus four new kiosk units. Space for outdoor dining will also be created. The existing shopping centre will remain fully open for the duration of the works.
It is anticipated that site work will start on the £30m scheme in spring 2013 with completion scheduled for summer 2014.
Approximately £4m will go on developing the external environment and public spaces around the centre as well as improved connections to Surrey Quays station and Canada Water tube and bus stations.
British Land retail development manager David Pollock 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. “