Plans for the bridge – designed by Thomas Heatherwick and promoted by Joanna Lumley – were revealed this summer.
The Garden Bridge Trust has been set up to raise the estimated £120 million-£150 million required to build the new river crossing between the ITV studios on the South Bank and Temple Underground Station on the north of the Thames.
On Wednesday the Government – as part of its National Infrastructure Plan – announced it will be contributing a large chunk of funding.
"We should remember that infrastructure can also add to the cultural life of our country, and our civic pride," said Rt Hon Danny Alexander MP, chief secretary to the Treasury.
"That's why the Government will be providing £30 million to help make the dream of a Garden Bridge over the Thames a reality.
"Providing this investment will – I'm certain – help the bridge's trust to secure private donations for the scheme, and move us closer to the target of a 2017 opening."
Transport for London has contributed £4 million to help get the project through the planning process.
"I have made a formal direction to TfL to undertake work on progressing the planning and feasibility of a new Garden Bridge across the Thames in Central London," said Mayor of London Boris Johnson earlier this Autumn.
"I did this because a new footbridge and open space in this location would help deliver my policies in relation to making and supporting the ongoing economic developments of London, as well as promoting walking by linking important London attractions.
"I consider an investment of £4 million to deliver a major piece of public infrastructure to be excellent value for the public purse."
• Public consultation on plans for the bridge continues until 20 December.
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