The news follows a decision by the EC that plans to lend funding for low-carbon projects did not break European state aid rules.
£3bn of government funds can now be used, but the permission has been granted on the condition that lending is restricted to low-carbon projects which cannot acquire funding from commercial markets.
GIB chairman Lord Smith said: "This is excellent news and a very important milestone as we transition to a low carbon economy and work to boost investment across the industry.
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"We have already made significant progress in building our teams and the necessary infrastructure for the bank and we expect to be fully operational in the next few weeks.
"We clearly have challenges ahead but we have the people, the expertise and the capability to deliver on our priorities and create the foundation for a new climate of green investment."
The banks’ headquarters are in the Scottish capital, where it will invest in innovative, eco-friendly areas across the UK which are experiencing a lack of support from markets.
The £3bn fund will be an initial injection and will extend from 2015 to borrowing through financial markets.
Projects targeted by the GIB will include offshore wind-power generation, waste-handling plants, energy efficiency measures, bio-fuels, biomass, carbon capture and storage, marine energy and renewable heat generation.
(IT)
