Construction of the new Garden Bridge over the River Thames could begin next year after the scheme was given the green light by the Mayor of London's office.
The tree-lined bridge between Temple Station and the South Bank has been designed by Thomas Heatherwick and was conceived by Joanna Lumley.
Sir Edward Lister said: "Having reviewed this application thoroughly, I am happy for Westminster City Council and Lambeth Council to determine the applications for the Garden Bridge themselves.
"We have worked hard with both local authorities and the Garden Bridge Trust to ensure that the bridge is of the very highest standard of design while remaining fully accessible to those who work, live in and visit the city."
Lord Davies, chairman of the Garden Bridge Trust, said: "Today's decision is fantastic news.
"As well as being London's newest and most imaginative green space, the Garden Bridge also brings wider benefits, such as reducing pedestrian journey times, creating a new route that avoids busy roads and providing jobs in construction and operations.
"There will also be dedicated education and volunteering opportunities. We are now looking forward to working with people to create a footbridge which adds to the capital's rich and diverse cultural heritage, to become a celebrated part of London's landscape."
£60 million of public money will be spent on the £175 million scheme. A total of £110 million has been pledged to date.
Westminster's planning committee imposed a condition on planning permission for the crossing requiring the Garden Bridge Trust to demonstrate that the bridge's maintenance costs will be underwritten by an organisation with substantial financial means such as Transport for London.
Boris Johnson said at Mayor's Question Time this week that there were no plans for TfL to be the bridge's guarantor: "I can confirm that no such agreement has been made, nor will I make any such undertaking to do so," he said.