The deal, which has a $175m (£108m) enterprise value, will see 3i take a stake alongside management.
JMJ has a host of businesses units dotted throughout the world, in places as diverse as Kazakhstan and Austin Texas.
Its European business unit is headquartered in Chiswick, west London. The business offers consultancy services to the manufacturing and construction companies across the globe, specialising in safety and compliance issues.
Simon Borrows, chief executive of 3i, said: “We continue to see attractive investment opportunities, particularly businesses with a strong international footprint.
“We are pleased to be investing in JMJ Associates, which operates in a high growth sector where we have extensive experience and knowledge.”
Shares in 3i, which was founded by a group of banks in 1945 as the Industrial and Commercial Finance Corporation, were flat on the news, rising only slightly to close up 0.1 per cent. 3i has been repositioning itself as a debt management and infrastructure investor in recent times after hitting troubles with its lagging share price.
Alan Giddins, managing partner at 3i private equity, said: “We have significant experience of the end markets in which JMJ operates and have a strong track record of working with consultancy businesses, so are well placed to work in partnership with management to take advantage of the sector’s exciting growth opportunities.”