Kelleher spent 15 months in the role after arriving from Morrisons in July of last year.
According to The Grocer, Asda chair Allan Leighton informed Asda employees that Kelleher was leaving the business with immediate effect.
The report added that Kelleher is leaving the retailer in order to pursue new opportunities.
“We can confirm that Matt Kelleher has left Asda today,” an Asda spokesman said.
“After more than 15 years in senior executive roles at Asda and elsewhere, Matt has decided the time is right to pursue a new direction. We wish him well for the future.”
Kelleher spent more than 11 years at Morrisons prior to joining Asda, working in a variety roles including as group technology and supply chain director.
As Asda’s first ever chief digital officer, Kelleher lead on the Project Future initiative.
The Grocer added that Asda is using the departure of Kelleher to restructure its hierarchy.
This includes current chief information officer Marcus Shaw and chief technology officer Adrian Berry taking on shared responsibility for Asda’s IT and systems teams.
Meanwhile, the supermarket’s online and analytics team under Barney Burgess, will now move into the customer team and report directly into chief customer officer Rachel Eyre.
