About 200,000 women could be in line for payouts averaging £13,500 to top-up the underpayment of their state pension for up to two decades.
The Department for Work and Pensions (DWP) revealed details of the underpayments on Wednesday.
The errors focus on automatic cash increases for certain married women, widows and over-80s dating back to 1992 with "enhanced" pensions.
The DWP estimated the bill for tackling the shortfalls to be about £2.7bn.
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The underpayment relates to the "old" state pension system - affecting those who reached pension age before 6 April 2016 - which had special provisions for married women.
Under these old rules, married women who had a poor pension in their own right could claim a 60% basic state pension based on their husband's record of contributions.
However, some of these pension were not automatically increased at a certain point.
"The action we are taking now will correct the historical underpayments that have been made by successive governments and anyone impacted will be contacted by us to ensure they receive all that they are owed," a spokesman for the DWP told the BBC.
A review will now take place involving the assessment of hundreds of thousands of cases, which could take many months to complete. It will include cases where the underpaid retiree has since passed away.
The issue was highlighted last year after former pensions minister, Steve Webb, tabled a freedom of information inquiry that revealed large numbers of women were being paid state pensions below the expected rate.
Special investigations unit
The DWP set up a special unit employing more than 100 civil servants to investigate the issue, and on Wednesday disclosed the full scale of the problem.
The scale of the underpayments came to light in the details of a report by fiscal watchdog the Office of Budget Responsibility (OBR) report which was published alongside the Budget.
It said: "The underpayment affected married women whose husbands reached pensionable age before 2008 and who were unknowingly entitled to 'enhanced pension' that would have boosted their payments by up to 60%.