Pensions payments will change to their intended levels from next month
About 5,000 retired public sector workers who have not been paid their full pension entitlement, some of them for decades, are to be reimbursed.
The Cabinet Office said they had been underpaid for periods ranging from a few months to 20 years.
The government does not yet have a final figure for how much money will have to be given.
An estimated 95,000 retired state workers have been overpaid but will not have to hand any pension money back.
The correct pension amounts - for those who have been overpaid and underpaid - will be notified to people from next month.
Some will see their monthly amounts increase, while others will see a reduction.
It was revealed last December that an estimated 95,000 public sector pensioners had been overpaid £126m since 1978.
About 5% of civil servants, teachers, NHS workers, judicial and armed forces personnel have been given an extra £1,300 on average.