The tower will seem to disappear into the sky
On the banks of the Thames, the London Bridge Tower will soar 1,000 feet (305 metres) above London and become Europe's tallest building.
It will house offices, hotels, homes, shops and restuarants adjacent to London Bridge station and has been backed by Ken Livingstone, Mayor of London.
Heritage groups, however, have objected to the skyscraper saying it would spoil views of historic City buildings, including St Paul's Cathedral.
The proposed tower, which has been designed by architect Renzo Piano, will appear as a slender spire of glass with steeply sloping faces made of large shards of "extra white glass".
This combination will make the tower seem partly to disappear into the sky and it is likely to change its character and appearance with seasonal variations of light and weather.
There will be three public viewing areas in the tower, including the top three floors.
A large, canopied, public space at the bottom of the tower will also be created under the scheme which will be on the current Southwark Towers site.
Southwark Council said it was likely the tower, which will be 200 feet (61 metres) higher than the UK's current tallest building, Canary Wharf tower, would become a symbol of London.
It has received the backing of the Greater London Authority which has drawn up policy on skyscrapers in London.
It did not believe that St Paul's Cathedral or other nearby heritage sites would be damaged by the skyscraper plan.
The Commission for Architecture and the Built Environment (Cabe), the government design watchdog, has also praised the proposal.
Cabe said the building "would inevitably assume iconic status.
"It would be visible from near and afar, from many different places, dominating many views.
"It would become a picture-postcard image representing London."
However, English Heritage, said the Tower of London World Heritage site would be compromised by the skyscraper which would be visible from inside the fortress.
It said views of St Paul's Cathedral from north London would be dominated by the skyscraper and Tower Bridge and other nearby historic buildings would be dominated by the tall building.
The man behind the ambitious scheme says the building is needed to provide office space in the City.
Entrepreneur Irvine Sellar said: "There is a shortage of quality office space, but more than that I think London deserves a global landmark of this sort."
Southwark Council's development control committee gave approval for the skyscraper at a meeting on Monday, with conditions.
Although the government has the right to call the application in for greater scrutiny, a spokeswoman for the council said it was thought unlikely because of the backing from the mayor of London.