Designed by Atkins, the building will house more than seven million books and journals in a low-oxygen environment along 262 kilometres of 'high-density, fully-automated shelving'.
The new depository will be used to help store an ever-growing number of items which the library has promised to keep in perpetuity.
Each year the library has to find room for an additional 12.5 km of shelf space at its existing headquarters in St Pancras and at other locations around London.
Once complete the Boston Spa facility - which will be built by contractor Allenbuild - will be home to low- and medium-use books and will sit alongside the British Library's existing buildings on the rural site.
Barry Paschali, a director of Atkins, said: 'As architects and engineers on this leading-edge building, the project has presented us with a fascinating challenge - to create sophisticated, innovative designs which fulfil complex requirements and complement the surrounding environment.'