It comes after The Telegraph first revealed details of the payroll crisis earlier this year, which was pushed through by bosses despite the risk of failure.
An Asda spokesman said: “We are supporting colleagues who were overpaid earlier this year by offering phased repayment plans of up to 12 months.
“We have communicated the repayment process and steps through line managers and to representative bodies including the GMB.
“We will also support any colleagues that need more time to make the repayment and they should speak to their line manager to arrange this.”
The supermarket has also rejected claims of cost-cutting across its IT structure, as it said the retailer is investing £800m to disentangle its systems from Walmart.
It follows an investigation this year that revealed that almost 10,000 workers had received incorrect payslips after the upgrade.
Some staff found themselves short hundreds of pounds, while others were overpaid.
This led to store managers making petty cash payments to those who were underpaid.
Asda’s finance chief Michael Gleeson later apologised for the problems, and said the company was sorry for the “anxiety” they had caused.
The changeover had been overseen by Mohsin Issa, who co-owns Asda and has been managing the business since 2021.
Asda has been on the hunt for a new chief executive, with The Telegraph revealing this month that the business is touting a lucrative package of between £8m and £10m for Mr Issa’s replacement.
It comes despite wider cost-cutting across Asda caused by debt pressures.
Figures last week from industry group Kantar revealed Asda was the only major supermarket to report a drop in sales for the 12 weeks to June 9.
This led to its market share slipping to 12.8pc down from 13.7pc a year earlier.