Southwark Council's planning committee has unanimously voted to back the 'spectacular' 24,000m2, heavily glazed project to the south west of the famous gallery in London's Bankside.
Among the concerns about the project was the possible loss of 'symmetry' of Giles Gilbert Scott's iconic - but still unlisted - former power station when viewed from across the Thames.
According to C20, 'the extension is felt to be lopsided and inappropriate for its sensitive context'.
The objections, which were formally handed to the committee, went on to say: 'While the Tate building makes a very strong and clear statement, the new high-rise buildings in the vicinity of the Tate are incoherent and a hotch-potch.'
Stamp was even more critical, claiming that the scheme was 'not only pretentious, excessively domineering and ill thought out in itself, but will gravely damage Giles Scott's building both physically and aesthetically.'
Meanwhile, the Greater London Authority also raised fears about the quality of the completed extension, stating that 'the application material is not convincing that the proposed combination of architecture and materials will deliver a world-class building.'
Nevertheless, Tate supremo Nicholas Serota was understandably elated by the outcome. He said: 'We are delighted that [the] committee voted unanimously in support of the scheme.
'This decision would not have been possible without the involvement and support of local residents which has been crucial to the development of the design. We look forward to bringing to Southwark a landmark building for the 21st century.'
Although the decision could yet be reviewed by London Mayor Ken Livingstone, it is unlikely the result will be queried - the London Development Authority has already invested £7 million to kick-start the development and 'help fast-track the scheme so that it might be completed in time for the Olympics in 2012.'