The gallery, due to open in May 2000, will be Britain's first national modern-art gallery and will show 20th-century works, with the Tate Gallery at Millbank devoted to a history of British art.
Lars Nittve, the Swede who will run the modern-art gallery under the overall Tate director, Nicholas Serota, was present yesterday at a topping- out ceremony at Bankside. He said discussions were continuing over which works would be displayed. They would be a mixture of 20th-century art from the Tate Collection and new commissions. But the new gallery would certainly contain a room devoted to the American abstract expressionist Mark Rothko. Giacometti and Brancusi will also be exhibited.
Among individual paintings to be displayed will be David Hockney's A Bigger Splash and Picasso's Three Dancers. "The Picasso is one of the five major Picasso paintings in the world," said Mr Nittve. "It's an extraordinary painting. If you want to make your dream exhibition, then it must be in it."
He added that the current crop of young British artists would be represented, with Hirst certain to be there, though it was not known which of his works would be on display.
The conversion of the power-station includes a glass structure running the length of the building that provides natural light and gives views of St Paul's Cathedral and beyond across London. Visitors entering the building go into the vast former turbine hall, which will give space for large art installations. The main galleries for works of art will be arranged on three of the seven levels, with a restaurant on the roof.
Mr Serota said: "The Tate Gallery of Modern Art is already beginning to change London's skyline. It is our belief that it will also change people's horizon on the future. We have maintained a steady course and are confident that we will meet both our timetable and our budget."
Nick Raynsford, minister for London, who was at the topping-out yesterday, said: "The impressive but redundant power-station is being transformed into a vibrant gallery which will, I am sure, become a jewel in the crown of London's reviving south bank." He added that a riverboat service would by the year 2000 be taking visitors to and from Bankside, and would stop at the Tate at Millbank, where a pier has yet to be built.
The original power-station, designed by Giles Gilbert Scott, is being transformed into the modern-art gallery by Swiss architects Herzog and de Meuron.