Smith, who had been on a secondment to the UK since 2012, is yet to finalise his new role at Walmart. He will be succeeeded by Barry Williams who will lead marketing at the retailer.
Williams is set to be replaced by Andrew Moore, currently responsible for George and general merchandise.
Asda also announced a number of other management changes including the appointment of a new MD for George, Nick Jones.
Asda President and CEO, Andy Clarke, said: "A retail business runs in cycles and as we start the year – one which promises to be the toughest year yet for our sector – I want stability at the top of the organisation through fewer, bigger leadership roles which will speed up decision making in this highly competitive market.
"Barry has driven our food trading operation with incredible skill and passion over the past two years. His absolute focus on doing the right things for our customers meant he was the natural choice for me to promote into the critical role of Chief Customer Officer as Steve completes his assignment with us."
Williams joined Asda in 2009.