Major plans for Tanks
The development will see the construction of a 65 metre high tapering tower almost double the size of the gallery, creating 5,000 square metres of extra display space.
Plans also include new terraces, offices and cafe facilities.
The project received a £7m donation from the Greater London Authority and a £50m Government investment, the largest amount to be received by a cultural project since the British Library.
The second phase is scheduled for completion in 2016.