The new book storage facility will be built alongside the Library's existing buildings at the Boston Spa site. It will provide additional storage for 7 million items from the UK national collection.
The new building will house books and journals currently stored at several locations around London. The overall move - including construction work - is valued at £25 million.
Atkins is the architect and multi-disciplinary engineers on the project with Capita Symonds as the project manager for the scheme.
Enabling works are underway with construction set to start on site at the end of July. Completion is expected in summer 2008.
The British Library's main site is at St Pancras in central London.