Hodgkinson spent two and a half years as digital and financial services director at Asda, where he oversaw Asda.com, Asda Direct and Asda Financial Services.
His other high-profile roles have included business development president at EMI and chief executive of Virgin Money.
Hodgkinson will replace former HMV marketing director Graham Sim, who left the company for Penguin, and incumbent e-commerce director Steve Napleton, who is leaving the business with immediate effect.
The appointment comes as HMV looks to transform itself into a broader entertainment brand and revamp its stores with a new trial format.
HMV Group chief executive Simon Fox said today (9 September) in a trading update that the group's trial Fast Forward stores have seen sales growth, adding the new store format will be rolled out to the majority of its 150 stores this month.
He said: "In technology, like for like sales in our initial six 'Fast Forward' stores have continued to grow by over 100%, and during the first quarter we have been preparing our enhanced technology offer, the benefit of which is not included in our first quarter.
"The roll-out of these space changes to the majority of the 150 stores takes place during September, and is on track to be completed at the beginning of October."
The retailer has been going through a torrid time, with like for like sales down 11% and a post-tax loss of £121m in the year to 30 June, forcing it to close stores and sell off bookstore chain Waterstone's.
But according to the update the group’s events division, HMV Live, is seeing signs of improvement, with attendances at events up by 20% on a like-for-like basis over the summer festival season.
HMV Live hosts festivals including Lovebox and Wilderness Music Festival and owns venues including the newly opened HMV Ritz, a 1500-capacity venue in Manchester.
During the quarter ending 3 September, the group also completed the disposal of HMV Canada and Waterstone's and secured a £220m refinancing deal.
In the interim statement, Fox concluded: "Overall, our plans for the Christmas trading period are on track, and we are focused on providing HMV customers with the very best offers across all of our product categories and live venues."