Speaking on LBC radio, Khan gave his support for the project in exchange for several demands being met. He wants to see the Garden Bridge made more open to the public, and said he wants "no more of London taxpayers' money, that I'm responsible for...spent on the project".
"What I think is really important is that I try and negotiate the best deal for Londoners."
He raised several concerns including the number of days the bridge will be closed for private functions, which will be used for fundraising.
"I've said to the Garden Bridge Trust, it's got to be less than the 12 days [per year] you're talking about. I am concerned when the bridge is closed, it's closed from midmight to midnight; that's not good enough. It's got to be much more open to the public."
Khan also called for the trust to work more with local schoolchildren to get them involved in the planting and maintenance of the bridge's gardens, and for seeds and plants grown on the bridge to be used in parks across the capital.
And he promised to publish the business plan for the bridge, which was produced under former mayor Boris Johnson, saying: "The early days of this project clearly fell short of our expectations on transparency. I am determined to run the most open and transparent administration London has ever seen. I will let the sunshine in, which is why we are today publishing the previously undisclosed full business plan for the Garden Bridge alongside a list of its funders."
A spokesman from the Garden Bridge Trust spokesman responded: "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.
"We share the Mayor’s desire to have the Bridge open to everyone for as long as possible. Balancing this and the need to raise the required private funds to operate the Bridge is important.
"We also share the Mayor’s desire to involve young people. We already have a Youth Board made up of over 40 local students, who will be taking an active role in developing our education and schools programme. We are also progressing partnerships with local green initiatives and charities and look forward to developing these further and building on the Mayor and the Trust's shared aspirations."