Southwark Council Planning committee has given the green light to the proposed 11-storey, £215 million extension designed by Herzog & de Meuron.
The new design uses a brick lattice effect that is more energy efficient and more closely relates to the Bankside Power Station behind it, than the previous glass construction.
Demolition works should start in July, with the majority of construction works commencing on site in January 2010. The Tate Modern 2 could be open by 2012.
Committee chair Councillor James Gurling said: “This challenging and iconic extension will not only help people move around the exhibitions in more comfort but also guide them outside to enjoy the lovely public space beyond to the Bankside and other parts of Southwark.”