The firm, which is run by billionaire brothers Mohsin and Zuber Issa, was acquired in a £6.8 billion deal with US supermarket Walmart.
TDR Capital now owns a majority share in Asda, with Walmart retaining an equity investment in the business and a seat on the company board.
The TDR Capital deal follows a failed bid to merge Asda with Sainsbury’s. That deal was quashed by the Competition and Markets Authority in 2019.
Roger Burnley, chief executive of Asda said: “This new ownership opens an exciting new chapter in Asda’s long heritage of delivering great value for UK shoppers.
“With our combined investment, expertise and ambition; Asda, Walmart, the Issa brothers and TDR have an incredible opportunity to accelerate our existing strategy and develop an even more exciting offer for our customers as well as strengthen our business for our colleagues.”