The GIB acquisition was made in two parts. A 44% stake of the project will be owned by the GIB's dedicated offshore wind fund.
The move completes Centrica's pull-out from offshore wind, announced in July 2015.
The fund, which now owns shares in six offshore wind assets worth £1.12bn, was set up to "provide long-term institutional investors with the opportunity to access the UK's green infrastructure sector".
In two rounds of funding, it has brought in investments from sovereign wealth funds and pension firms including Swedish group AMF Pensionsforsakring AB and the UK-based Strathclyde Pension Fund.
"In setting up an offshore wind fund GIB has created an innovative way to connect deep pools of long term capital to UK green infrastructure projects. In a short period of time we have successfully raised our first fund and fully invested its capital, passing our £1bn target," said GIB chief executive Shaun Kingsbury.
The fund is managed by GIB Financial Services, a subsidiary of the currently state-owned bank. GIB will hold the remaining 31% itself and 25% is still owned by Danish developer Dong Energy.
Dong has also announced it will take on the operations and maintenance services of the project. Centrica, which is currently responsible for the site, will hand over the O&M activity 12 months after the transaction is completed.
Lincs has been in operation since 2013. Its 75 Siemens 3.6MW turbines are installed 8km off the UK's east coast.
GIB's offshore wind fund also owns portions of the Lynn and Inner Dowsing, Gwynt y Mor, Rhyl Flats and Sheringham Shoal projects, amounting to more than 1.1GW of the UK's offshore capacity.
The GIB is currently in the process of being hived-off by the UK government, with widespread reports that infrastructure firm Macquarie set to buy the institution.
The UK government has recently come under pressure from parliament to delay the sale of GIB, with critics arguing it could lose its green credentials under private owners.
Green Party MP Caroline Lucas told a House of Commons debate: "The preferred bidder, Macquarie, not only has a dismal and terrible environmental record but an appalling track record of asset-stripping. So why has the government given preferred bidder status to this company?"
Department of Business, Energy and Industrial Strategy (BEIS) minister Nick Hurd said he was unable to comment on any company rumoured to be in discussions of a takeover but defended the sale of the bank.
"Potential bidders are interested in the GIB precisely because of its green specialism. We are asking potential investors to confirm their commitment to GIB's green values and investment principles, and how they propose to protect them, as part of their bids for the company," he told parliament.
"We want to ensure that the GIB can be reclassified to the private sector, but we have also been clear that we want to move it into the private sector to enable the business to grow and continue as an institution that supports investment in the green economy.
"We are selling it as a going concern, and potential investors would have to buy into the company's green business plan and project pipeline. These are the criteria that we have set and against which we are evaluating the proposals before us," he added.
Backed by £3bn of funding from the UK government, the GIB became fully operational in October 2012.
It was tasked with funding low-carbon infrastructure projects in a bid to attract private investment. Offshore wind has been a core focus of the bank.