The British Library is to set build an "exciting and distinctive" 12-storey extension, with extra galleries, commercial space and shops.
Camden Council has approved the £500m development, which is expected to be finished by 2029.
The new building will have two new entrances and better access to St Pancras Station.
However, some local residents are worried the tower will block light to their homes and cause light pollution.
The new building is set to include two basement levels and house an extra 100,000 sq ft (9,300 sq m) of library space, learning, business and events spaces, according to the Local Democracy Reporting Service.
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.
The development must also make space for infrastructure for the proposed Crossrail 2 rail link, and a pedestrian walkway will run the length of the basement to a new ticket hall.
Camden's planning committee approved the scheme, which has to pay for itself without any funding from the government, which means it has included some commercial space.
The Somers Town Neighbourhood Forum, which represents some local residents, has expressed concern about the impact of the scheme on a nearby estate.
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 for residents.
Camden's principal conservation officer, Catherine Bond, said they were "what you would expect in dense a urban environment".
The meeting heard 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 for approval.
Follow BBC London on Facebook, Twitter and Instagram. Send your story ideas to hellobbclondon@bbc.co.uk
The race for space at the British Library
The British Library
Camden Council
Man faces jail for fatal attack on banking boss in the West End
My London: MP Emily Thornberry
Camden New Journal Food & Drink Thrilled customers raise their glasses to the Tamil Prince
Ibrahim Bah killing: David Joseph Johnson convicted of manslaughter for Greenwich stabbing
King Charles and Queen Consort to visit east London, palace says
Luxury flat owners win landmark case over window-peeping Tate Modern tourists
Putin: 80 years on, we are facing German tanks again
Republicans oust Ilhan Omar from House committee
Tyre Nichols rumour fits victim-blaming pattern
Russian army officer: Our troops tortured Ukrainians
US secures deal on bases to complete arc around China
Why TikTok has got us talking about mascara
Can Sri Lanka trade its way back to prosperity?
How the empire of one of the world's richest men lost $100bn
Why ballroom dancing thrives in Asian communities. Video
Helena Bonham Carter on soaps and sexism
Why lifting opposition ban suits Tanzania's leader
The world's most influential school?
A remedy for low motivation and passion
The 90s cop show that changed TV
How one volcano could make global chaos
© 2023 BBC. The BBC is not responsible for the content of external sites. Read about our approach to external linking.
