The acquisition was part of a final investment decision by E.on on the project. E.on has committed to spending £1.3 billion on the project. GIB will take a 19% stake in the project, with E.on holding on to the remaining shares.
The investment will be used to construct and maintain the project, situated 13 kilometres off the Sussex coast. Onshore construction of the project is expected to begin next month, with offshore activities due to commence in "early 2016", according to E.on.
Rampion will the first Round Three project to begin construction in the UK. It is expected online in 2018.
Following the investment, MHI-Vestas confirmed an order from E.on to supply 116 V112-3.45MW turbines to the project.
The Rampion project was originally planned to be 700MW, but was cut in size in November.
E.on development manager Chris Tomlinson said at the time the reduction in size was to "optimise the scheme in the best seabed conditions".
The Green Investment Bank has now supported seven offshore projects in the UK. Walney, Rhyl Flats, London Array, Gwynt y Mor, Westermost Rough and Sheringham Shoal have all benefited from its support.
Last month, the bank secured £463 million of investment to support offshore projects.