Around 37,000 current and former Argos workers are to receive an average of £64 each after "incorrect" payments were discovered.
Sainsbury's, which took over the high street chain six months ago, said the workers had been paid below the national living wage.
This related to the timings of staff briefings before they had clocked on to their shifts, and security searches which could happen after workers had finished a shift.
The payments will be made at the end of this month, at a total cost of £2.4 million.
The 37,000 figure includes 12,000 who currently work in Argos stores.
John Rogers, chief executive of Argos, said in a letter to staff that "unexpected things" cropped up, adding: "After we acquired the Argos business last year it was brought to my attention that, as part of a routine visit, HMRC had uncovered an issue with some of our Argos store systems and processes, which means that some colleagues have been paid below the national living wage.
"In particular, this related to the timings of colleague briefings, which could happen before colleagues had clocked into their shifts and security searches, which could happen after colleagues had clocked out of their shifts.
"Sainsbury's prides itself on being a trusted brand where people love to work and I was, therefore, very disappointed to hear this and launched an immediate investigation."
He said new processes had been introduced to ensure there can be no repeat of the issue.
"We concluded our conversations with HMRC last week and are telling Argos store colleagues this week that, where they were paid below the national living wage prior to December 2016, they will receive a payment on February 28 for the amount owed to them."
The announcement came after the Government named and shamed 360 businesses for underpaying thousands of workers a total of almost £1 million.
The biggest ever list of offenders included employers in hairdressing, retail, hospitality and care homes.
Excuses for underpaying workers included using tips to top up pay, docking wages to pay for Christmas parties, and making staff pay for their own uniforms.
Retail giant Debenhams was accused of failing to pay almost £135,000 to just under 12,000 workers.
The company said it made a technical error in its payroll calculations, which resulted in an average underpayment of around £10 per person to affected workers in 2015.
Dave Gill, national officer of the Usdaw union, said: "We have been in talks with the company to get this situation resolved as a matter of urgency.
"Our members in Argos are clearly disappointed to have been underpaid and we are seeking safeguards to ensure that this cannot occur again."