The Corporation of London's planning committee has given the green light to Grimshaw's 50-storey Minerva Tower.
Planning experts believe the decision leaves the tower 'moreor-less' free to start on site because, in the wake of the London Bridge Tower inquiry, the ODPM is unlikely to call it in.
In a statement, Minerva's chief executive Andrew Rosenfeld said he was delighted with the decision. 'This is a major achievement not only for Minerva, but also for the City of London.
'It is fitting that this magnificent tower, which will redefine the City's skyline, has been created by a British developer working with a leading British architect, ' he added.
But the capital's conservation lobby has attacked the decision.
Paul Drury, planning adviser to the Historic Royal Palaces, said he was 'extremely disappointed but not surprised'.
'We were expecting the decision to go the way of the developers since London Bridge Tower got the go-ahead, ' he said.
'But it doesn't mean we are not disappointed about the serious impact it will have on the Tower.'
Adam Wilkinson of SAVE Britain's Heritage agreed. 'If the Shard of Glass is going to be a spike through the heart of London, then this is more like a juggernaut.
'However, I do not expect it to be called in because English Heritage are not going to push for it, ' he added. 'They are not interested in incurring the wrath of John Prescott again. They are still feeling bruised after the London Bridge Tower battle.'