The Government is selling the Green Investment Bank to Australian firm Macquarie for £2.3 billion.
Ministers said that, under the new ownership, at least £3 billion will be invested in the green economy over the next three years.
The bank was launched in 2012 to channel investment into low carbon development.
Climate Change and Industry Minister Nick Hurd said: "The Green Investment Bank has been very successful in attracting private capital to the UK's green economy.
"It now makes sense to move it into the private sector where it will be free from the constraints of public sector ownership, allowing it to build further on its success."
Lord Smith of Kelvin, independent chairman of the Green Investment Bank (GIB), said the board had supported the decision to privatise the Government-backed bank as the best route to securing its long-term future and growing green impact.
He said: "There is a compelling logic in the world's first green bank joining forces with the world's largest infrastructure investor.
"When we embarked on this process, we were determined to find a new owner who would build on GIB's successful history - an owner who would have access to deep pools of capital, a commitment to expand GIB's activities, and a respect for the unique role GIB has played in the market.
"Macquarie will bring all of this to GIB, along with its own impressive track record of green investments.
"Its vision for the future growth of GIB demonstrates a redoubling of its commitment to a low-carbon economy."
But Doug Parr, policy director at Greenpeace UK, labelled the sale to the Australian firm "a disaster".
"At a time when the Government should be shoring up low-carbon industry for post-Brexit Britain, they have given away one of our key tools for advancing green technologies.
"The hole left by the Green Investment Bank will slow our transition to a clean energy system, set us back on reaching our climate targets, and mean more of the jobs from new sectors will go elsewhere."
Since it was formed, the bank, set up with money from the taxpayer, has invested in projects ranging from offshore wind farms and council LED street lighting to replacing boiler systems in sheltered housing, hydropower schemes, energy from waste plants and energy efficiency investments in distilleries.
The bank has supported almost 100 green infrastructure projects, attracting £3 of third party capital for every £1 invested.
Mr Hurd said the deal was the "best of both worlds", securing value for the taxpayer, while investment in the green economy will increase.
"GIB has a well-funded new owner that is committed to the bank's green mission, with a track record of success in green investment and an ambition to grow the business."
The sale means all taxpayer-funded investment in the bank, including set-up costs, has been returned with a profit, said the Government.
The bank's brand will be maintained, and the new owners said they will utilise the skills of employees in Edinburgh and London.
The office in Edinburgh will be home to a new green energy business.
David Fass, chief executive of the Macquarie Group said: "The addition of the Green Investment Bank, its people and expertise, strengthens Macquarie's commitment to the green energy sector.
"Our combined platform will build on the legacy of the Green Investment Bank and, alongside our knowledge of energy and infrastructure, will open further opportunities in low carbon investment both in the UK and further afield.
"We are excited by a business that will take a leading role in the green economy using the specialist knowledge of our teams in Edinburgh and London."
Former energy secretary Sir Ed Davey, who is seeking a return to Parliament, said the sale was "environmentally irresponsible, and on the eve of the election is politically dubious".