Around 49,000 former and current WINZ clients who were underpaid because of a coding error will be back paid, Social Development Minister Anne Tolley says.

The error affected clients who received Accommodation Supplement payments in 1993. They were owed $29m in total.

The Ministry of Social Development (MSD) estimated the average reimbursement would be around $590.

However 48 clients would get $10,000 or more, with one retiree netting $28,500.

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The error came to light after Tolley asked MSD to review its practices to ensure they were in line with legislation.

"While we can't go back and change an error from 23 years ago, the Government is doing the right thing by everyone affected," she said.

Current clients would get their lump-sum reimbursement, along with an apology letter, by the end of the year.

Former clients can find out if they are eligible from next week by visiting the MSD website. They have at least six months to apply for their reimbursement.

The coding error also resulted in 65,000 clients being overpaid by a total of $53m. But they won't have to pay back the money.

Tolley said the reimbursements wouldn't affect the recipients' benefit payments, because the payments will be excluded from asset-testing for 12 months.