The proposed 367-metre bridge set to span the river between the South Bank and Covent Garden was granted planning permission by Lambeth Council by five votes to two in a meeting last night.
The design, which will feature two fluted piers supporting a promenade of trees and shrubs, now needs a thumbs up from Westminster City Council to move forwards. The borough is expected to review the plans before the end of the year.
On hearing the news Thomas Heatherwick commented: "The Garden Bridge will be an extraordinarily special place, either to race across, relax in or look back at the rest of the city's sights. It is fantastic that the Lambeth has helped London take one step closer to making it a reality."
The bridge will cost £175 million to build – a sum that has provoked criticism. Observer columnist Rowan Moore described it as a vanity project that needs to prove it is worth spending public money on, above other deserving causes.
"The more you look at the proposed Garden bridge over the Thames, the less sense it makes," he said.
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A petition launched by campaign group Thames Central Open Space opposing the scheme has attracted almost 800 signatures. These critics claim a park would be better suited elsewhere in the capital.
In the meeting Heatherwick said the project was all about "creating new and extraordinary views of London framed by nature", which he believes can only happen in the city centre. "If you put this over Battersea, you don't see the heart of our incredible city."
"This is the perfect and right place to build this most incredible project," he told the council. "We're in the thought-leading capital of the world and right at the geographical centre of that city is the biggest gap in the rhythm of the crossings across the river."
The Garden Bridge is expected to begin construction next year to avoiding clashing with the proposed Thames Tideway Tunnel, which is due to start in 2017.