The Leeds-based retailer, which was bought by the Issa brothers and private equity backers TDR Capital for £6.8bn last year, has confirmed that Lord Rose will take up the role next month.
The retailer has also appointed Dame Alison Carnwath, a director at EG, to be a non-executive director at Asda.
Lord Rose, who was chair at Ocado until last year, said his priority will be to find a new chief executive to lead Asda as it continues its transition with its new owners.
Former chief executive, Roger Burnley, left the supermarket group ahead of schedule in August, leaving the business without a successor in place.
“I am delighted to be appointed chair of Asda, one of the biggest and best retail businesses in Britain,” said Lord Rose.
“I am joining the board at a hugely exciting time, as Asda builds on the incredible resilience it has demonstrated during the pandemic and embarks on the next chapter of its evolution and growth under new ownership.
“I am pleased to be joined on the board by Dame Alison, who brings rigour and focus to everything she does, and look forward to confirming further non-executive appointments to our board in the near future.
“We are both excited at the prospect of working with Mohsin and Zuber and the wider Asda team as they look to build on Asda’s strong heritage of delivering affordable quality across food, fashion and general merchandise – and of championing customers at every turn.”
Dame Alison Carnwath said: “I am delighted to be joining the board of Asda as a non-executive director.
“Asda plays an important role in the daily lives of millions of consumers across the UK and I am looking forward to working with Lord Rose, Mohsin and Zuber Issa and the entire Asda team to support the business as it builds on strong foundations to drive growth.”
In a joint statement, Mohsin and Zuber Issa said: “We are committed to ensuring this iconic business has the right governance and management framework in place to set it up for long-term success.
“The appointment of Lord Rose and Dame Alison mark an important step forward in this ongoing process and we plan to appoint further independent non-executive directors in due course.”