TFG, which also owns Hobbs, Whistles and Phase Eight, is understood to be paying around £50m for the business.
The new owner said it plans to further expand White Stuff’s portfolio of stores and concessions following positive recent growth for the brand.
The retailer, which was founded in 1985, has 113 stores and 46 concessions in the UK, with a further six stores and 25 concessions across Europe
Revenue for the business rose to a record £154.8m in the year to April.
White Stuff chief executive Joe Jenkins will continue in the role, while founders George Treves and Sean Thomas will step down from the board and exit the business.
Justin Hampshire, chief executive of TFG London, said: “With White Stuff’s strong presence on the high street and significant potential for sustained growth, we are committed to supporting Jo and her talented team with their ambitious rollout strategy for further growth of the store and concession properties.
“At the same time, TFG London will continue to invest in the White Stuff brand and online offer to drive further awareness and growth.”
George Treves, co-founder of retailer White Stuff, said the sale of the company to TFG was “significant and emotional” for him and co-founder Sean Thomas.
“Today marks an important and emotional milestone for Sean and me. We spent over 40 years building this company from the ground up,” he said.
“While this decision was not easy, we believe it is the right next step for White Stuff and know that TFG is committed to providing White Stuff with new opportunities for growth.”
Jo Jenkins added: “This is a very exciting time for White Stuff and represents the natural next step for our business.
“It builds on the hard work and success the brand has achieved over the past years. TFG London is the perfect owner for our business.
“They value our brand, have extensive premium retail experience and will be excellent long-term owners to support White Stuff’s next phase of growth.”