Peyton and Byrne will take on the running of the public and staff restaurants at the library, staff "grab-and-go" bar, coffee bar The Last Word and conference and banqueting provision, when the contract commences later this month.
The deal is believed to involve capital investment in facilities from the caterer.
It marks the end of more than a decade's involvement with the library for Compass Group, which most recently ran services at the site under its Leith's brand.
The British Library's main site is at London St Pancras, which it moved to from the British Museum in 1998, but it also has a site in north London's Colindale dedicated to newspapers, as well as Boston Spa in Wetherby, North Yorkshire.
It holds some 14m books, 920,000 journal and newspaper titles, 58m patents and three million sound recordings and its three sites in the UK welcome 400,000 people a year to its reading rooms.
Oliver Peyton's Peyton and Byrne also runs the National Dining Rooms in the National Gallery, a public restaurant at the Wallace Collection and a bar and café at the Institute of Contemporary Arts, all in London.
By Chris Druce
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