However, Mr Khan demanded the scheme must be made "more accessible" to all Londoners.
The planned £175 million green footbridge will link Temple with Southbank in the city.
Describing the project as one that could rival New York's High Line, the Mayor warned the Bridge "must be a genuinely public and open space for all Londoners, rather than a closed and private space".
Mr Khan has put forward a series of amendments the Garden Bridge Trust must include in exchange for his continued support:
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• The Bridge to be closed for fewer days each year for private fundraising events – the current plans are for 12 closures a year
• The Bridge to be closed for fewer hours each time it has to close for fundraising events, so that the Bridge can still be used in the morning and evenings – the current plans are for it to be closed from midnight to midnight
• A guarantee that children at local schools on either side of the river will get to visit the Garden Bridge and be involved in planting and maintenance – with a rolling programme of events for local school children
• The Garden Bridge Trust to "build a strong working relationship" with all of London's parks, so that seeds and plants grown on the Garden Bridge can then be replanted in parks across the capital.
A Garden Bridge Trust spokesperson said: "We welcome the Mayor's support and look forward to working with him and his team to make the beautiful Garden Bridge happen and deliver its many benefits to millions of Londoners and visitors to the city."
(LM/JP)
