Financial details were not disclosed, although a report in the UK’s Telegraph newspaper in April suggested the business could sell for up to £900m.
TDR said it planned to invest in DLL to “enhance the member experience and cement DLL’s market leading position”.
AltAssets reported in April that private equity firms were circling DLL, with Blackstone, Apax Partners and Advent International named by Telegraph.
The business was owned by Caird Capital and London & Regional, which backed a 2007 buyout led by current chief executive Scott Lloyd, the heir to former English tennis professional David Lloyd who founded the chain.
TDR founding partner Manjit Dale said, “DLL is a unique business with a market leading position and a fantastic brand.
“We look forward to investing capital in order to further improve the member experience and to attract new members.
“We believe that DLL will be a great first investment for our latest fund, TDR Capital III, drawing as it does on our experience of growing first class leisure businesses in the UK for the benefit of members, staff and investors.”
TDR held a €900m first close for its third buyout fund last month according to Dow Jones, which cited two people familiar with the matter.
Earlier this year AltAssets reported that the firm expected to hold a final close before the end of the year, although there was no specific timetable.
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