Northern Rock Asset Management (NRAM) - the state-owned part of the defunct lender - is to refund a total of £270m to customers.
The bank will pay an average of £1,775 to each affected customer after failing to disclose information in documents and letters in 2008.
The Chancellor told Parliament that 152,000 customers who had loans below £25,000 were affected and blamed "an error originating in 2008 when Northern Rock was in public ownership".
"Some customers with certain types of mainly unsecured personal loans were not given all the mandatory information in their statements which they were entitled to by law," George Osborne added.
The chief executive of UK Asset Resolution - NRAM's holding company - Richard Banks said: "We are determined to do the right thing for customers and the taxpayer.
"We will be writing to all customers who are affected and advising them on next steps."
Northern Rock was split into two separate companies in 2010 – Northern Rock plc, which was sold to Virgin Monday earlier this year, and NRAM.
At the height of the financial crisis, the troubled bank was forced to rely on funding from the Bank of England to keep it from collapsing
Treasury Economic Secretary Sajid Javid said the refunds are "likely to increase public sector net borrowing for 2012/2013".
But he added that they are "not expected to delay materially" the timings of NRAM's repayment of £19.6bn Government funding.
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