The gallery said the ziggurat-shaped glass building, due to be completed in time for the 2012 London Olympics, would almost double the facility's exhibition space.
The expansion will be financed through a combination of public and private funding, including 7 million pounds (US$13 million, Ђ 10 million) from the London Development Agency.
It will be built by Swiss architects Herzog and de Meuron, who created the gallery from the disused Bankside power station, the AP reports.
Designed to accommodate 1.8 million visitors a year, the gallery now gets more than 4 million, Tate director Nicholas Serota said.
The 70 meter (230 foot) structure will include 10 new galleries and two performance spaces. It will be built on the site of an electricity substation on the south side of the gallery.
He said the gallery was confident of raising the money to complete the project on time.
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