The Design Museum will remain in the building until the move in 2015.
Deyan Sudjic, the museum's director, said: "Whilst we are sad to be leaving Shad Thames we are leaving the building in the best possible hands..."
In a statement, Hadid said the building would be an opportunity "to consolidate our archive in a single location". It would also be used for architecture exhibitions where "the research and innovation of global collaborations in art, architecture and design" could be put on display. — guardian.co.uk