Brockwell was previously a director at financial services advisory firm Global Capital Finance, where she was responsible for the firm's European renewable energy transactions, including offshore wind.
She will lead the delivery of an expanded offshore wind investment strategy that sees GIB move into providing funding for new offshore wind facilities that are in the construction phase, as well as for existing wind facilities.
Speaking about the appointment, GIB chief executive Shaun Kingsbury said: "The development in our offshore wind strategy will ensure that we can mobilise investment at a critical, early stage of a project."
Brockwell said: "Through its direct funding capabilities and its desire to stimulate co-investment from other institutions, the GIB is vital to the industry's success in realising its planned installed capacity."
During its first five months of trading, up to 31 March 2013 the GIB committed less funding to offshore wind than any other priority sectors.
This could change if a recently announced memorandum of understanding between the bank and Abu Dhabi clean energy firm Masdar leads to further deals to fund UK offshore wind projects.
The GIB's two offshore wind transactions to date have been a £46 million contribution to a debt refinancing deal for the Walney project and £57 million for a quarter stake in Rhyl Flats.