Sadiq Khan has lent his support to the Garden Bridge so long as it is more accessible to "all Londoners".
The newly-elected London mayor said the planned £175m footbridge linking Temple with the Southbank "must be a genuinely public and open space".
Mr Khan, who has previously questioned the project's transparency, insisted on amendments in exchange for his support.
The Department for Transport and Transport for London have each invested £30 million in the project.
Mr Khan, said: "The early days of this project clearly fell short of our expectations on transparency.
"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."
Sadiq Khan's demands include:
•The bridge to be closed for fewer than 12 days each year for private fundraising events
•The Bridge to be closed for fewer hours when it closes for fundraising events - the current plans are for it to be closed from midnight to midnight
•A guarantee children from local schools will get to visit and be involved in planting and maintenance
•The Garden Bridge Trust to build a strong working relationship with all of London's parks
Questions were raised in March when it was revealed Transport for London officialsmet the designer of the planned bridge four times before the procurement process began.
Caroline Pidgeon, Liberal Democrat London Assembly Member, said Mr Khan's decision was "highly disappointing" and he should be seeking to recoup all Transport for London funding allocated to the project.
Caroline Russell, Green Party London Assembly Member, has also expressed her disappointment in the move.
"The Garden Bridge should be scrapped and the Mayor should focus on delivering bridges in East London where people need routes for walking and cycling across the river," she said.