The Garden Bridge Trust has announced that the proposed footbridge between the South Bank and Temple "cannot be delivered" and the charity will be wound up.
The trust has blamed a lack of support from Mayor of London Sadiq Khan for the failure of the project.
Lord Davies, chairman of the trust, said: "It is with great regret that trustees have concluded that without Mayoral support the the project cannot be delivered.
"We are incredibly sad that we have not been able to make the dream of the Garden Bridge a reality and that the Mayor does not feel able to continue with the support he initially gave us.
"We had made great progress obtaining planning permission, satisfying most of our planning conditions and we had raised £70 million 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.
"It is all the more disappointing because the Trust was set up at the request of TfL, the organisation headed up by the Mayor, to deliver the project.
"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.
"I would like to thank our donors and supporters, who gave us unstinting help and support along the way."
Vauxhall MP Kate Hoey told the SE1 website: "I welcome the decision to end this project which never had any support from local residents.
"If only the GBT had listened from the beginning to the views of those living in the area a great deal of public money would not have been wasted."
The Mayor of London, Sadiq Khan, said: "It's my duty to ensure taxpayers' money is spent responsibly.
"Following the very serious issues highlighted in Dame Margaret Hodge's independent review of the bridge – including a funding gap of over £70 million, potentially unlimited costs to London taxpayers to fund the bridge in the future, systemic failings in the procurement process and decisions not being driven by value for money – I could not permit a single penny more of London taxpayers' money being spent on it.
"I have been clear since before I became Mayor that no more London taxpayers' money should be spent on this project and when I took office I gave the Garden Bridge Trust time to try and address the multiple serious issues with it.
"Londoners will, like me, be very angry that London taxpayers have now lost tens of millions of pounds – committed by the previous Mayor – on a project that has amounted to nothing"
One of the stumbling blocks to constructing the bridge was a failure to reach agreement with Coin Street Community Builders over the use of land on the South Bank.
"A lot of time and money has been expended by many public and private bodies on this project and it is important to learn some lessons," said Coin Street chief executive Iain Tuckett.
"It is right that a great city like London should look to realise ambitious and visionary projects but we need to focus not just on the cost of creating these projects but also be realistic about the ongoing costs of managing and maintaining them so that deliver their promised public benefits.
"In the case of the Garden Bridge, questions about the real costs of ongoing management and maintenance – and who should bear them – were initially avoided and eventually addressed too late."
Last week we reported that the trust had attempted to find a third party to provide maintenance guarantees to satisfy the conditions attached to the planning permission.
Political scrutiny is now likely to be applied to how around £50 million of public money has been spent on the project without a brick being laid.
Conservative London Assembly member Andrew Boff argues that the Mayor should have withdrawn his backing from the bridge sooner.
"Sadiq Khan had all the information necessary to cancel this project in May last year. As Lord Davies' letter makes clear, however, his inability to make decisions has cost the public purse £9 million.
"His predecessor, wrongly in my view, clearly supported the plans for the Garden Bridge. It's clear that Sadiq Khan's indecision has wasted millions more pounds of taxpayers' money in the confusion.
"As we await the publication of transcripts from Margaret Hodge's secretive Garden Bridge review, the Mayor must now answer further questions about his contribution to this disastrous project."