The development control committee made the decision on Monday when it agreed that the building would be an asset to the capital.
The committee's report said: "There seems to be very wide agreement, even among those opposing the siting of the tower at London Bridge, that this proposal is a supreme example of world-class architecture."
Supporters include architectural watchdog CABE and London mayor Ken Livingstone. CABE said it could become "a picture postcard image representing London".
The decision to grant planning permission comes in the same week that the Government Office for London also agreed Hammersmith and Fulham council's decision to allow developer Chelsfield's £1bn retail development in White City, west London.
The Ian Ritchie-designed scheme is a flagship project. The council's deputy for regeneration Dame Sally Powell said: "Now that the White City development has been given the final go-ahead, this will boost the overall regeneration of the north of the borough, which is under way."
Support for the two schemes comes as doubts continue over the £1.5bn Elephant & Castle regeneration project in south London.
A contract between Southwark council and developer Southwark Land Regeneration (SLR) is expected to be put to a council committee on 26 March.
With less than two weeks to go, the two parties are still working out the financial details. Southwark cabinet member for regeneration and economic development Steve Lancashire said: "There are still issues of commercial terms. The terms are significantly different from what SLR wanted in the middle of last year."
Originally SLR was to redevelop housing at the scheme's Heygate Estate site, but the council decided that the developer's demand of a 20% rate of return was too costly, and is to appoint a registered social landlord to carry out the works.
SLR director Nicholas Taylor said: "The local authority wanted to change the local housing procuring arrangement to make more money."