Brait said it will buy a 90 percent stake in New Look for 780 million pounds ($1.23 billion), putting the retailer at an enterprise value of 1.9 billion pounds.
"Brait will fund the purchase consideration using facilities and cash on hand," the company said in a statement.
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New Look Chief Executive Anders Kristiansen told reporters in February that the retailer was ready for a stock market flotation, though that decision was up to the owners.
New Look pulled a planned stock market listing in 2010 amid turbulent financial markets.
In April Brait bought an 80 percent controlling stake in gym group Virgin Active for $1 billion, seeking to tap the growing health-conscious middle classes, particularly in Africa and Asia.