The company has added more than 40 restaurants since RCP first invested in 2004, with 3i paying £10m for a minority stake in the fast-growing business two years later.
That investment valued the company at £24m, and was used to roll out more restaurants and allow early angel investors to exit the company.
3i said it made a 1.6 times money multiple selling its 36.8 per cent stake.
Giraffe, which provides global cuisine alongside world music, announced record profits last summer, with turnover increasing 18 per cent to £40m and EBITDA rising 17 per cent to £4m.
The first Giraffe opened in Hampstead, North London in 1998 and the group now consists of 48 sites nationwide, including franchised sites at Heathrow and other UK airports as well as one in Dubai.
3i director Justin Maltz said, “We saw the potential early on for [managing director Russel Joffe] and his team to take their successful London high street concept and expand it across both geography and location types.
“This investment has been a great example of 3i’s ability to back entrepreneurs to significantly scale up their business, by providing growth capital alongside the founders via a minority equity stake.
“It has been great fun working with management and the board to create a distinctive and scalable brand, bringing the unique Giraffe hospitality to customers across the UK – and now internationally.
“We know the team remains ambitious to further grow the business under Tesco’s ownership and we look forward to their continued success.”
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