He joined the retailer in 1993 and played a central role in Wal-Mart's acquisition of the grocer. However, Asda's growth has slowed in the past six months.
Despite the recent slip in performance, DeNunzio claimed his time at the supermarket had been a success. He said: 'After 12 rewarding years at Asda, I leave one of the most successful retail businesses in the UK in the hands of a strong management team. Now I'm looking forward to working with the Vendex KBB team to deliver profitable growth.'
A statement from Asda thanked DeNunzio for his contribution to the company. He will leave in the 'next few weeks' and the retailer said it will announce a replacement shortly.
Asda's chief operating officer Andy Bond is expected to be one name in the frame.
Commenting on the grocer's performance in TNS data on market share, Andrew Fowler said: 'Asda increasingly looks stuck in a strategic and trading cul-de-sac. Against easing [comparable sales] TNS says Asda is seeing only low-single digit sales growth, in-line with the overall market and much slowed from last summer despite the acquisition of ex-Safeway space.
The non-food led momentum appears to have been extinguished and we sense Asda is suffering from greater competition for the hearts and wallets of its core customer constituency from the expanding Morrisons.'