The bridge would connect Temple with the South Bank, with backers the Garden Bridge Trust saying it would create a new public space in central London as well as providing a new crossing over the Thames.
Last year the Mayor authorised TfL to make “a small investment” of £4m to help cover planning and feasibility studies.
TfL has worked with GBT to help develop the concept “a developed design that is capable of being submitted for full planning permission.”
Mr Johnson has now instructed the transport agency to contribute £30m towards the £159m project, matching a promise of a further £30m from central government.
The Mayor’s authorisation is confirmed in a document published on the City Hall website on Friday afternoon.
The document says the Trust will be required to raise the remaining funding “from high net worth individuals, charitable trusts and commercial organisations”.
Government and City Hall money will be paid in stages, with up to £8m made available from each in the “pre-contract phase.”
The document warns that “if the project does not proceed beyond the stage, this funding will be at risk.”
It adds that GBT will need “demonstrate that is has secured, or is able to secure, the balance of funding required to construct the Garden Bridge,” before the remainder of the public cash is handed over.
The bridge will be open to all pedestrians, including those with restricted mobility, but according to the document, will be closed to cyclists.
Applications for planning consent were submitted to Lambeth and Westminster councils last month.
