The Garden Bridge was originally estimated to cost £60 million ($78 million, 71 million euros) but the figure rose to more than £200 million, with a funding gap of at least £70 million.
A review found that £37.4 million of public money had already been spent and it would cost taxpayers £46.4 million in total even if it was scrapped, but recommended this was a better option than risking exposure to further costs.
Khan said that under the previous mayor, Foreign Secretary Boris Johnson, a lot of taxpayers' money had already been spent on the bridge and Khan had always said no more should be allocated.
He said London faced being left with a half-built bridge that it would either have to complete or demolish if the plans were allowed to go ahead.
"The funding gap is now at over £70 million and it appears unlikely that the trust will succeed in raising the private funds required," he said.
"I am simply not prepared to risk a situation where the taxpayer has to step in and contribute significant additional amounts to ensure the project is completed."
The bridge would have crossed the Thames between Waterloo and Blackfriars bridges, linking the Temple area with the South Bank.
The Garden Bridge Trust which was running the project intends to fight on but faces a major challenge to find another organisation to take on the responsibility.
"We have had enormous support from our funders and are very confident we can raise the remaining funds required," said Trust chairman Mervyn Davies.
Copyright Agence France-Presse, 2017