The UK energy company's joint venture partner Siemens Project Ventures has also agreed to sell its 25 per cent share to the bank, while Dong Energy, another partner, will continue to hold its 25 per cent share.
Centrica will continue to provide operations and maintenance support to Lincs for a 12-month transitional period, following which Dong Energy will take over of the wind farm which is located off the east coast of England at Skegness.
The Green Investment Bank will own a 31 per cent stake in Lincs, while its Offshore Wind Fund will hold 44 per cent. The fund manager now has assets under management worth £1.12bn.
Centrica, which owns British Gas, said its net share of the proceeds will be approximately £220m. It first said it would withdrawal from windpower generation to shift towards end-consumer services in 2015, according to Reuters. It will continue to buy power from renewable energy firms, however.
Centrica's shares edged up more than one per cent at the market close.
The transaction is set to be completed in February 2017.