When Tate Modern first opened in the disused Bankside power station seven years ago, the gallery tentatively hoped that it might attract 1.8 million visitors a year. Now more than 5 million trek through annually, with the crowds sometimes making even its cavernous Turbine Hall seem cramped.

The Government yesterday rewarded the Tate’s success in becoming the most popular museum of modern art in the world by announcing a £50 million grant of taxpayers’ money to go towards an enormous £215 million building that will be constructed next door.

The grant was described as the largest capital commitment by government to a cultural project since the British Library – a slightly unfortunate comparison because the library went £450 million over budget and opened 15 years late.

The Tate hopes to attract an extra million visitors a year with the new building, which will more than double its existing space and enable more of its huge collection to be shown. At present, up to 60 per cent of the Tate’s paintings and sculptures are in storage, although it rotates its holdings.

The new building is a futuristic, higgledy-piggledy glass structure that features huge blocks protruding from a ziggurat which the Tate’s director, Sir Nicholas Serota, believes will become a “spectacular” landmark for the city.

Designed by Jacques Herzog and Pierre de Meuron – the Swiss architects who turned Sir Giles Gilbert Scott’s original 1940s building into Tate Modern – it will adjoin Tate Modern to the south, on the site of the former power station’s oil tanks.

With its completion planned for 2012, in time for the Olympics, the initial design divided expert opinion.

Daniel Libeskind, whose own extension for the Victoria and Albert Museum was abandoned, described it as “a wonderful project”, and Rowan Moore, director of the Architecture Foundation, said that “it has the potential to be a very dramatic building”. However, Gavin Stamp, the architectural historian, dismissed it as “bloody stupid and pretentious”. He said: “It is spoiling Scott’s great cathedral of power. It involves the demolition of the symmetrical south facade. With the money to serious arts being cut due to the Olympics, I’m dismayed to hear that money has been found for this. Isn’t the Tate big enough?”

Sir Nicholas said that the extension was vital for the continued success of the Tate. “There is serious overcrowding in the galleries, particularly at weekends, and there is an urgent need to improve and extend facilities,” he said.

The Tate will construct “different kinds of galleries” to show art forms that are new to the gallery, including photography, video, film and performance. Around 60 per cent of the visitors are under the age of 35. “That tells you a great deal about the appetite for contemporary art,” Sir Nicholas said.

“Today’s announcement is an important endorsement by government of the contribution that the arts make to society as a whole and the importance of British art at an international level. This commitment confirms London’s position as one of the leading international centres for the visual arts.”

James Purnell, the Culture Secretary, said that he had fought the Tate’s case with the Treasury. Asked what arguments he had used to persuade them that £50 million should be spent on a gallery, he said that the arts were a vital part of Britain, that they made people happy and that the Government was “funding hospitals as well”.

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