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."
Back in April, Khan refused to commit further public funds to the bridge after it was revealed £37.4 million of public money had already been spent, without building work even starting.
With the UK's economy going through a difficult time since the Brexit referendum and the continuing uncertainty over the country's finances once the Brexit process is completed, many believed it was a waste of public money, particularly when the NHS is struggling.
Khan asked Labour MP Margaret Hodge to review if the bridge was value for public money, she recommend the project be scrapped, suggesting it would cost over £200million to build.
Since it was first announced three years ago, it had been criticised as a 'vanity project' of then-Mayor Boris Johnson, who famously championed the Emirates Air Line cable car from North Greenwich to Docklands, which has very low passenger usage.
Johnson and fellow bridge supporters claimed it would bring tourism to the South Bank, despite the area already bustling with tourists.
The bridge would have connected the Temple area to the South Bank - despite Waterloo Bridge and Blackfriars Bridge being a 5 minute walk away in either direction.
Many questioned the need for a bridge in the centre of London, when so many motorists were crying out for more river crossings further east down the Thames.
Although it was touted as a bridge for the public to enjoy, many Londoners were upset when it emerged it would be closed off on occasions for private events.
Locals were also unimpressed that Transport for London would be contributing to the bridge, when TfL justify their annual fare rises on the need to upgrade the tube and increase capacity.
Some critics had claimed the annual costs to maintain the Garden Bridge alone would dwarf the rest of the capital's river crossings' fees.
There were also fears the bridge would ruin protected views from Waterloo and Blackfriars Bridge.
In a statement on Monday, the Mayor said: "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."
Johnson, who previously declined to assist in Hodge's review of the project, tried to put the blame on Khan for the end of the project, claiming the bridge would have been "easily financed", despite the Trust's struggle to find financing.
He said: "So sad Sadiq Khan has killed Garden Bridge and wasted so much time and money. Labour has no vision for London and no ambition."
BBC London's transport correspondent Tom Edwards said: "It was never really a transport project, it was a tourist attraction and crucially in 2012 no-one asked locals if they wanted it."
Name that bridge!
Name that bridge!
Art critic and philosopher Alain de Botton likened this bridge in England's south west to a 'stocky middle-aged man who hoists his trousers and loudly solicits the attention of others before making a jump between two points.' Hmm....
Overlooking Bristol and the Avon Gorge, Clifton Suspension Bridge was designed by Isambard Kingdom Brunel and was completed in 1864, five years after his death. It spans 702 feet and is considered one of the finest engineering feats in British history.
For hundreds of years this bridge in Northern Ireland was used by fishermen to gain access to a small island whose waters were brimming with salmon...
These days flocks of tourists have replaced hopeful fishermen on Country Antrim’s Carrick-a-Rede Rope Bridge- whose name means ‘rock in the road’. The salmon have dwindled, but fine coastal views attract ramblers from all over the UK.
The rural Shropshire valley dominated by this bridge - the first of its kind in the world - has been granted UNESCO status, owing to its historical significance as ‘The Birthplace of the Industrial Revolution’.
Upon its completion on New Year’s Day, 1781, Ironbridge became the world’s first, ahem, iron bridge. It overlooks the Ironbridge Gorge and village, whose factories used to produce more engines, wheels, rails and iron goods than anywhere else in the world.
This historic suspension bridge hops over to a barren island known in the local language as ‘Ynys Môn’. In the background looms the tallest mountain range south of Scotland.
The island is Anglesey, the mountain range is Snowdonia and the bridge is Thomas Telford’s Menai Suspension Bridge, completed in 1826, which straddles the Menai Straits in Wales’s north-west.
An iconic dome and one of the world’s trendiest art galleries are connected by this pedestrian-only affair, made of steel, and designed by one of our most eminent contemporary architects...
The iconic dome is that of St Paul’s Cathedral, the trendy gallery is the Tate Modern, the architect is Sir Norman foster, and the bridge, of course, is the London Millennium Footbridge, which was completed in 2000.
This toll bridge links a Welsh border town famous for its horse races to an English county notable for an orange-coloured cheese.
Severn Bridge spans the Severn Estuary, linking the Welsh town of Chepstow and the English county of Gloucestershire. Strangely, passengers are only charged upon crossing from the English side.
One of the great London icons, it was constructed in 1894, has big neo-Gothic towers and looms over the River Thames beside the Tower of London...
Tower Bridge, made from Cornish granite, Portland stone and 11,000 tonnes of steel. At the time of construction, its trademark raising bascules- allowing river traffic to flow underneath- were a technological revelation.
This compression arch suspended-deck bridge is the best known of seven bridges crossing a famously foggy river...
Tyne Bridge overlooks the trendy BALTIC art gallery on Newcastle’s Quayside. Although there has been a bridge here since Roman times, the current structure dates back to 1928.
This bridge dominates the riverfront of a city forever associated with its Roman baths and Georgian townhouses. Based on a famous Italian bridge, it is one of only four in the world spanned by shops on either side.
The city of Bath is home to Pulteney Bridge. Designed by Robert Adam and inspired by the Ponte Vecchio in Florence, it was completed in 1773.
It might look like a row of giant tin openers, but this rotating boat-lift bridge ingeniously connects two of Scotland’s main canals.
The Falkirk Wheel makes it possible to transfer shipping between the Forth and Clyde Canal and the Union Canal. The bridge is now such a national landmark that you can see a picture of it on one side of a Scottish £50 note.