As part of the deal, LDC’s Richard Whitwell and David Bains will join the operator’s board.
Among its travel portfolio, LDC also has investments in Iglu.com and Blue Bay Travel.
Neilson operates beach clubs, ski hotels and chalets and 65 yachts, exclusively for its guests who number almost 80,000 each year.
The sale sees Risk Capital Partners relinquish its stake in the operator after originally investing in 2013, backing Neilson chief executive David Taylor and chairman Richard Bowden-Doyle to acquire the brand from Thomas Cook.