The project is expected to be completed in 2012
Tate Modern's proposed £215m extension has been given the green light by planners, the London gallery has said.
The 11-storey, brick and glass structure - designed by Swiss architects Herzog and de Meuron - will increase capacity at the gallery.
Southwark Council approved the revised project for the extension which is expected to be completed in 2012.
Tate Modern said £74m had already been raised towards the extension - a third of the overall cost.
Tate director Sir Nicholas Serota said he was "delighted" the plans had been approved.
In a report, Southwark Council said: "The proposed new building will be an extraordinary and unique addition to London's townscape.
"There have already been great regeneration benefits for the area following the opening of Tate Modern at Bankside."
The council originally gave the extension the go-ahead two years ago, but Tate Modern revised the plans and replaced the glass-covered cube design, with the current pyramid-like structure clad in perforated brick.
It will lead directly into the Turbine Hall and the interconnecting spaces will become the "foundation" of the new Tate Modern.
Sir Nicholas said: "We look forward to creating one of the most exciting cultural buildings in Europe which will bring direct benefits to Southwark and London as a whole."
The Tate said the project will also address some of the strains on the current building.
The gallery was originally designed for two million visitors a year but nine years after it opened to the public, that figure is nearer five million.