The Garden Bridge Trust has informed mayor of London Sadiq Khan, Transport for London (TfL) and the Department for Transport that it will be winding up the project.
Lord Mervyn Davies, chairman of the Garden Bridge Trust, said: "It is with great regret that trustees have concluded that without mayoral support the project cannot be delivered.
“We had made great progress obtaining planning permission, satisfying most of our planning conditions and we had raised £70m of private money towards the project.
"The Garden Bridge would have been a unique place; a beautiful new green space in the heart of London, free to use and open to all, showcasing the best of British talent and innovation.
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“It is a sad day for London because it is sending out a message to the world that we can no longer deliver such exciting projects.”
Earlier this year, Mr Khan confirmed that the Greater London Authority was not prepared to sign the guarantee for the annual maintenance costs of the Bridge.
At the time, Mr Khan said: “Under the previous mayor, a considerable amount of London taxpayers’ money has already been spent on the Garden Bridge.
“I have always been clear that not a penny more of taxpayers' money should be allocated to the project.”
Planning permission for the project is due to end this year.
The bridge was set to be located between Temple and the South Bank and was initially budgeted in 2014 to cost £150m.
Since Mr Khan’s announcement, the trust has had discussions with a potential benefactor and the government, which came to nothing.
The Garden Bridge project will now be formally closed, which includes terminating contracts and concluding donor funding agreements associated with the project. The Trust will then be wound up in accordance with the Companies Acts.