The deal brings to an end 50 per cent ownership of the 133-year-old fund house by its employees, and an exit for US private equity group Crestview which took a then 24.9 per cent stake at the peak of Currie's growth in 2007.
Since then assets have more than halved, though last year the firm bounced back from its first ever loss following £8.8 million of regulatory fines in the UK and US in relation to its now sold private equity business in China.
Willie Watt, Martin Currie chief executive, said: "We approached Legg Mason to talk to them about distributing our products in the US, and they came back to us with a proposition that was much more far-reaching.
"They have got £700 billion under management but they don't actually have an international equities business.
"The head office in Edinburgh is retained, with total autonomy in terms of how we run the investment floor."
The Herald reported last August that the group's annual accounts showed that the internal share price, used in group share schemes that account for part of the 50 per cent employee stake, had fallen in 2011-2012 from £15.50 to £3.10.
Mr Watt said the terms of the deal were not being disclosed, adding: "It's an exit for our institutional shareholders, and everyone is I think reasonably happy with what has been done."
When Mr Watt took over in March 2002, he had hopes of growing Currie's assets from £6.1 billion to match those of neighbour Baillie Gifford, then at £20 billion - and now at more than £100 billion.
He said: "I think since 2012 we have had really strong asset growth and we are well on the way to rebuilding the business.
"We can now rebuild it quicker."
On his record, he said: "I'm sure all of us if we look back over a ten-year period would have things we would do differently, but I am pleased that we have the choice to drive this partnership forward.
"Our long-term plan was to rebuild our business organically, and our shareholders have always been very supportive….it wasn't so much that we were in any way daunted, it's just that this opportunity is the right one for us."
Legg Mason said the deal would bring Currie into "affiliate" status alongside six other groups it has acquired, and senior management at Martin Currie had signed long-term contracts providing "strength and stability".
It said Legg Mason Australian Equities with $2.5 billion in assets and a 14-person team - would become part of Martin Currie, which had assets under management of £5.8 billion at June 30.
Joe Sullivan, Legg Mason's chief executive and president said: "We believe that, over time, our global retail distribution platform will be able to meaningfully leverage Martin Currie's broad-based investment capabilities."
Steven Forbes at Alan Steel Asset Management in Linlithgow said: "It's sad that a venerable Edinburgh institution has now moved into foreign hands.
"I would have thought their market share was dwindling, and this should enable them to beef up their performance."
He said Legg Mason was becoming "quite aggressive", had a good international equity income fund, and would make a growing impact in the market.
Graeme Forbes, at financial planners Intelligent Capital in Glasgow, said: "In financial service now it is all about consolidation - it should be a good thing for everybody because scale is important."