UK Business Secretary Sajid Javid has conceded there should be a block on any move away from funding green projects.
Unusually, the government is setting up an independent company to control that veto power.
The move is designed to ensure that there is a clear break from any government controls.
This has been necessary to meet European public accounting rules on government ownership and influence over private enterprises.
It follows discussions with the Office for National Statistics, which polices the application of these accounting rules in Britain.
The Edinburgh-based Green Investment Bank (GIB) is being sold to raise capital for the Treasury, reduce government borrowing, and to let it expand by borrowing in private financial markets.
This was announced last June, and is included in the Business Bill currently before parliament. The House of Lords amended the Bill to include the proposal for a "golden share".
After assessing the sale process, parliament's environmental audit committee raised a series of objections and challenges to the way in which it is being privatised.
These included a call for the business plan to be made public, for alternative ownership models to be investigated, and for the government to retain a minority share.
The business secretary has given ground on only the idea of a "golden share", saying it was not his preference, but was a response to parliamentary recommendations.
The business department's responses stated: "The government intends to approve the creation of a special share in GIB, with the right to approve any change to the green purposes of GIB, as set out in the objects clause of GIB's Articles of Association.
"The special share will be held by a separate company, independent of both GIB and government, created specifically to hold this special share."
More detail on who is to control the share, and how, is to be set out later.
Mr Javid commented: "Moving the Green Investment Bank into private ownership makes sense. If you want it to have access to more capital, to make bigger investments and have a bigger impact in green sectors it is the best course of action.
"To ensure the bank's green credentials are maintained, it plans to put a special share structure in place that protects its green mission and keeps it focused on what it does best."
Lord Smith of Kelvin, chairman of the GIB, said: "I have always been confident that any new investor in GIB will be strongly committed to our green mission - our commitment to, and expertise in, green investment is the very reason they would be investing in us.
"That said, I understand the concern among some of our stakeholders over the legislative changes, so I am delighted we have been able to offer them the additional commitment that a special share will bring."
GIB was launched in November 2012 - the first 'for profit' government-owned bank aimed at investing in environmental infrastructure.  It has had £3.8bn of Government capital injected, but was denied the ability to raise further capital in private markets.
It has a requirement to invest across five objectives; reducing greenhouse gas emissions, efficiency in use of natural resources, protection of the environment, protecting or improving biodiversity and promoting environmental sustainability.
Its investment decisions are also required to make a positive contribution to reductions in climate change.
So far, GIB has invested in 63 projects, committing £2.2bn into projects with a total value of £10bn.
These include waste plants, anaerobic digestion, wind farms, street lighting, heat pump installation, district heating projects, energy efficiency re-fits of hospitals and biomass boilers in whisky distilleries.
The environmental role of the Green Investment Bank, after it is privatised, is to be protected by a so-called "golden share".