Today’s announcement follows a decision by London mayor Sadiq Khan in April that no more taxpayers’ cash would go towards the bridge.
His predecessor Boris Johnson had allocated £60m to the project.
Pre-construction costs and legal fees have already cost the public purse £46.4m and will not be recovered.
Dame Margaret Hodge published a report in April – commissioned by Khan - on the venture which called for it to be scrapped because there were “too many things” wrong with it and it did not represent value for money.
Lord Mervyn Davies, chairman of the Garden Bridge Trust, has today written to the mayor, stating: "It is with great regret that trustees have concluded that without mayoral support 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.”
Davies claimed that the trust had made “great progress” in securing planning permission and raising £70m of private investment for the scheme - but this still left a £70m black hole in funding.
He said it was a sad day for London because it sent out a message that it could no longer deliver “exciting” projects.