Hubbard left BP last month after almost five years as UK convenience retail director running all of BP's convenience forecourt stores, including BP Connect, Wild Bean Café, and its joint venture with M&S Simply Food.
She will be responsible for Asda's 80 smaller stores, looking at how they can be developed and improved.
However, Asda dismissed suggestions Hubbard's convenience store background meant plans were afoot for a chain of Asda c-stores.
Hubbard is due to start work in the new year, reporting to Andy Clark, Asda's retail director. She replaces Colin Heggarty who will move to a project management role within the company.
Asda also announced this week that people director David Smith, who headed its HR department, would retire in the new year. Smith has been with the business for 15 years and was promoted to his current role in July 2000. Several policies introduced by Smith have been adopted by Asda's parent company Wal-Mart and are now used worldwide, including the 'stores of learning', which act as training hubs for staff.
During his time in the role, Asda won several awards including The Sunday Times' Best Company to Work For in 2001 and the Financial Times' Number One Place to Work in 2003.
"David will leave in the knowledge that Asda has the lowest turnover and absence rate across the retail sector and one of the most motivated workforces in Britain," said an Asda spokeswoman.
Caroline Massingham, retail people director for George and Asda's distribution arm, will take over until a successor is chosen.
Hubbard had led an "extraordinary transformation" of the UK business according to BP. During her time in the role she extended the number of joint BP Connect and Marks & Spencer Simply Food stores to 150.