Karren Brady, the West Ham United chief executive and star of TV's The Apprentice, is to become chairman of Taveta, the holding company for former BHS owner Sir Philip Green's retail empire.
Baroness Brady, who is a Conservative peer, is taking over as the prominent barrister Lord Grabiner confirms he is stepping down from the role.
Grabiner spent 15 years leading the Taveta board, which came under fire from MPs for providing "weak" corporate governance that contributed "substantially" to the demise of BHS.
Sky News reported in May that the chairman was on the verge of quitting.
Taveta is the company that owns Sir Philip's Arcadia retail empire, whose brands include Topshop, Dorothy Perkins and Burton.
Arcadia employs more than 24,000 people and has an annual turnover of more than £2bn.
Sir Philip owned BHS for 15 years before selling the loss-making retailer to Dominic Chappell, a serial bankrupt with no retail experience, for £1 in 2015.
It collapsed the following year with the loss of 11,000 jobs and leaving 20,000 pension scheme members facing an uncertain future.
Sir Philip came under severe criticism from MPs, who called for him to be stripped of his knighthood.
Earlier this year, he agreed to pay £363m to plug a hole in BHS retirement schemes.
Brady has been on the Taveta board as non-executive director since 2010.
Sir Philip said he was "delighted" to announce her appointment to chair the board, which she has assumed immediately, and thanked Lord Grabiner for 15 years of service.
Brady said: "I look forward to working with my colleagues as we concentrate on driving the Arcadia brands forward on their global expansion."
Baroness Brady is well known to television viewers as an adviser to Lord Alan Sugar on BBC reality show The Apprentice.
In 2013 she was named business ambassador by then prime minister David Cameron.
The Taveta announcement comes after the company's most recent annual results showed pre-tax profits falling from £172m to £37m for the year to 27 August last year.
Sales were down 2.5% while the business was also hit by costs linked to the collapse of BHS.