Clarke appears to be the latest casualty of the grocery wars. All the big four supermarkets have replaced their chief executives in the past two years.
Speaking to Retail Week, Clarke said he would remain in place at least until Burnley arrives in October. He did not give an exact date for stepping down, but indicated it was likely he would stay on after Burnley's arrival to help thrash out a succession plan. He may also take on a new role at Walmart, Asda's parent.
Asda poached Burnley from Sainsbury's last October, where he was retail and operations director, but a 12-month notice period means he cannot join until later this year.
Clarke is currently overseeing 'Project Renewal', Asda's five-year revival strategy, which entails price cuts, store changes and a refocus of its ecommerce efforts.
Clarke said on his departure: "I’m in no rush to do anything else.
"We’re on a three-year journey from a strategic plan perspective, I’m very happy to continue to deliver that and to work through that and see the strategic plan implemented. Then we can talk about it from there."
Despite aggressive price cuts, Asda has failed to fend off competition from German discounters Aldi and Lidl, whose market share in the UK continues to expand. The pair account for 10% of the UK grocery market, according to Kanter Worldpanel.
Its rivals are also performing more strongly. Like-for-like sales grew at Tesco for the first time in three years for its latest quarter and Morrisons returned to profit after Christmas. Sainsbury's, however, is expected to report a sales decline this week.