Sir George is responsible for overseeing and guiding the growth of Toscafund, which manages $4bn (£2.1bn) for City institutions and the very rich.
Martin Hughes, the former Credit Lyonnais Laing banking analyst who set up Toscafund in 2000, said: "Sir George has enormous experience of the workings of the world's financial markets and I have no doubt that his insight and advice will be tremendously valuable to us as we develop."
Sir George's pay for the part-time role was not disclosed.
Hedge funds, unlike traditional investment funds, are able to deploy a wider range of investment strategies across a broader range of markets and financial instruments in the search for better returns.
The number of hedge funds has soared from fewer than 500 managing less than $100bn in 1990 to more than 8,000 today with $1,500bn under management globally.
Toscafund runs a "long/ short" equity hedge fund, which invests in stocks that it expects to rise in value and also takes bets on other shares it thinks will fall.
The value of its long-only equity fund increased 48 per cent in its first year.
During two decades with RBS, Sir George built a parochial lender that was vulnerable to takeover into a global banking powerhouse valued at more than £66bn. Following the transformational £22bn hostile acquisition of a flabby National Westminster Bank in 2000, RBS is now the eighth-biggest bank in the world.
Profits were just £32m when Sir George became chief executive in 1992. Last year, RBS made £8.3bn.
Dunfermline-born Sir George, who played for his local Ballater rugby team well into his fifties, started out as an electrical engineer, then worked for the venture capitalists 3i before becoming chief executive of the Scottish Development Agency in 1981.
He joined RBS as director of strategic planning in 1987. Three years later, he took his rescue plan for the bank - later dubbed "Project Columbus" - to the then chairman, Sir George Younger.
That saw him become deputy chief executive, where he axed 3,500 jobs and brought a more commercial edge to the bank. He stepped down as RBS chairman last month.
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