The NAO scrutinised the government's £2.3 billion (€2.75 billion) sale of the bank, which completed earlier this year.
GIB was launched by the business department (BIS, now BEIS) in 2012 to invest in projects such as offshore wind farms, waste to energy plants and energy efficiency.
The UK government decided to sell the bank in mid-2015, just as it became profitable, attracting widespread criticism from politicians.
In April 2017, the government decided to sell the bank straight away, rather than pursue its original plan to phase the sale.
This decision was made despite the bank's internal valuations showing that its assets under construction could have been worth more when operational.
Following advice from its financial expertise body UK Government Investments (UKGI), the government concluded the potential benefits of a phased sale were outweighed by the risks, which included construction risks, the risk that an initial public offering might be unsuccessful, the risk that it might be unable to secure a state aid extension and the risk that a phased sale might require additional public funding.
However, the NAO's inquiry revealed that UKGI did not fully value the benefits and risks of its phased sale option until February 2017, after a number of key decisions had already been taken. It estimated the value of construction risk avoided at between £67 million and £98 million.
The NAO calculated that the amount lost in selling before assets were fully built at £63 million, but noted that this amount could have been considerably more or less depending on how successfully assets moved from construction to operation.
The NAO's scrutiny also found the business department lacked clear criteria or evidence to judge whether the bank was achieving its intended impact on investments in clean technologies.
The department also wanted GIB to be an "enduring institution" but did not make clear what this would mean in practice.
Overall, the sale process took nearly 18 months, more than twice the time anticipated. This was partly down to corporate restructuring, which members of the bank's board told the NAO was unnecessary and had distracted them from normal operations.
The delay also caused a number of key staff to leave the bank, which limited its ability to invest.
Buyer, Australian investment firm Macquarie, increased its commitments to the future of GIB following the direct intervention of its board. It committed to continue with the bank's green objectives for three years after the sale, though this is non-binding.
Amyas Morse, head of the NAO said: "Ultimately the value for money of the Green Investment Bank intervention will only be seen over time. A key test will be whether the government needs to intervene again in this way to stimulate growth in the green economy and to help it achieve its climate change commitments."
As of March 2017, the bank had invested in 100 projects, committing up to £3.4 billion of its own capital, and had attracted £8.6 billion of private capital, equating to around £2.50 for every £1 invested, according to the NAO.
Green Party co-leader Caroline Lucas, said that the waste of millions of pounds by the government by not going ahead with the phased sale was "simply shocking".
"Not only was the sale of the Green Investment Bank wrong in principle, but the whole process was carried out in a way that was hugely disappointing.
"Despite its clear success the Green Investment Bank was hived off to private equity firm, whose non-binding commitment to tackling climate change for just the next three years will do little to assuage people's concerns," she said.
A spokesman for BEIS said that the sale of the GIB made £186 million profit for the taxpayer, while removing the constraints of public ownership and allowing the bank to operate overseas as well as in the UK.
"Our valuation analysis took into account the risks of the holding assets and the maturity of GIB's portfolio. The sale of GIB offered a higher degree of certainty and Macquarie now bears the risks of GIB's projects under construction," he said.
The government will review the report's recommendations and respond in due course, he added.
MPs on the Environmental Audit Committee are to investigate whether the privatised bank is still fulfilling its green objectives as part of an inquiry into green finance.