The team behind the Gherkin plan to build “The Tulip” next door on Bury Street.
It will have a total height of 305.3 metres – making it the second tallest building in Western Europe after the Shard.
The City Corporation’s Planning and Transportation Committee gave the go-ahead by a vote of 18-7.
The Tulip will include a viewing platform with rotating pods, a restaurant and sky bar, cycle parking and shower facilities, a new pocket park at street level, publicly accessible rooftop terrace, and an entire floor dedicated to education facilities during school hours.
Planning Committee Chairman, Chris Hayward, said: “After a lengthy and robust debate, the committee agreed to approve this truly unique visitor attraction.
“One of my key objectives as Chairman of the Planning and Transportation Committee has been to enable the continued transformation of the City of London into a place which welcomes members of the public on weekends as during the week.
“This building has the potential to play an important role in realising our vision of the Square Mile as a vibrant 24/7 city.”