The British Library is to set build an 12-storey extension with extra galleries, offices and shops as part of a £500m development.
Camden Council has approved the project which is expected to be completed by 2029.
The new building will have two new entrances and improved access to St Pancras Station.
It will include two basement levels and house an extra 100,000 sq ft (9,300 sq m) of library space, learning, business and events spaces
It will replace the British Library Centre for Conservation and will also provide a new home for the Alan Turing Institute for data intelligence and artificial intelligence.
Camden’s planning committee approved the scheme which will not receive government funding so will include commercial projects.
The Somers Town Neighbourhood Forum, which represents some local residents, has expressed concern about the impact of the scheme on a nearby estate with some local residents worried the tower will block light to their homes and cause light pollution.
It is also worried about losing a community garden while the work takes place. A new community garden will open at the same time as the library extension.
Councillor Sue Vincent asked officers at the council meeting about the impact of the development on residents, the BBC’s Local Democracy Reporting Service reported.
Camden’s principal conservation officer Catherine Bond said they were “what you would expect in dense a urban environment”.
The council meeting on the plan was told the British Library will also make a £23m contribution to affordable housing in Somers Town.
The British Library’s chief executive Roly Keating said: “This long-planned extension will make it possible for even more people to access and enjoy the library, with a host of flexible new spaces including a new bespoke learning centre and spectacular new exhibition galleries.”
The plan now has to be referred to the Mayor of London Sadiq Khan for approval.