In his decision letter, issued this week, Prescott says that the proposal by Teighmore Ltd (Sellar Property) is "of the highest architectural quality".
Had this not been the case, he insists, he might have refused the application, "but the quality of the design is a very strong argument in its favour".
The proposal, dubbed the "Shard of Glass", is supported by the London Borough of Southwark and London mayor Ken Livingstone, but opposed by English Heritage, which argued at a public inquiry earlier this year that it would ruin protected views of St Paul's Cathedral and overwhelm local listed buildings.
But Prescott is satisfied that the 306m building "will reduce neither the visibility nor the setting of St Paul's" and that it will be "an enhancement of the present background". The location makes the proposal "very sustainable", he added.
Michael Crook, a partner at Cushman & Wakefield Healey & Baker, which provided planning advice to Teighmore, said: "The decision demonstrates that a well-designed tall building can be located in London."
However, an English Heritage spokesperson commented: "The tower would be an inappropriate addition to the skyline in the area. In no way does the decision signal a green light for tall building proposals in London."