McKenna, who has been with Asda 15 years, replaces Simon King who left suddenly last month after only six months with the supermarket.
From September she will take responsibility for Asda’s retail operations, including its stores, distribution network and IT systems.
Earlier this week it was confirmed that marketing strategy director Jon Owen has also left the chain to join Very.co.uk, the online fashion retailer owned by Shop Direct Group.
Owen, who had responsibility for advertising and marketing strategy and is credited with masterminding the Asda Price Guarantee, took on the role a year ago when Mark Sinnock defected after being in the role just 15 months.
Sinnock had joined from ad agency Fallon.
Chief executive Andy Clarke says that McKenna represents someone who lives Asda’s culture everyday.
He adds: “Her understanding of our business, her passion for people development, her down to earth style and ability to get things done, will all contribute to ensuring she is a great COO.”