Around 70,000 people are thought to have been underpaid benefits by an average of £5,000 each, according to the public spending watchdog.
Those affected were transferred to the employment and support allowance (ESA) from other benefits after 2011, the National Audit Office said.
NAO chief Sir Amyas Morse said many of the claimants have severely limiting disabilities and illnesses.
He blamed the Department for Work and Pensions for "failing to get a grip on the problem".
He added: "The department has now committed to fixing this error by April 2019, but not everyone will be repaid all the money they have missed out on."
A review of 1,000 sample cases found that around 45,000 people may be entitled to around £2,500 each, but 20,000 could be owed around £11,500 each and "a small number of people" could have been underpaid by £20,000.
As well as the arrears, which date back to 21 October, 2014, the Government will face higher ongoing payments due to the corrected claims.
The DWP said it would need to pay between £570m and £830m more ESA than previously expected by the end of 2022/23.
According to the NAO investigation, the DWP's process for moving people from benefits that were being phased out to the ESA "did not reflect its own legislation".
The problem was not recognised until 2014 and even then steps were not taken to correct the mistakes.
It was not until July 2017 that the DWP admitted it had a responsibility to find the people affected.
Since then, it has reviewed more than 4,000 cases and paid just over £9m to 1,500 people who were underpaid.
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A DWP spokesman said: "We're committed to ensuring people get what they are entitled to receive as quickly as possible.
"Everyone who could be affected will be contacted directly by the department."