Northern Rock is to be sold to Virgin Money in a deal worth at least £747 million, the government has announced.
The bank was taken into public ownership in 2008 at the start of the crisis in the banking sector.
Northern Rock was split into two separate entities: Northern Rock plc, a new savings and mortgage bank authorised as a mortgage lender by the FSA; and Northern Rock (Asset Management) plc.
Virgin Money is buying Northern Rock plc.
The Treasury said on Thursday the sale was "in the best interests of the taxpayer" and secured the long-term future of the company. It hopes to ultimately to receive more than £1bn from the deal.
But the taxpayer still stands to lose up to £650m from the deal, as it was initially bought for £1.4bn.
Richard Branson's Virgin Money has had to agree to a series of commitments in return for acquiring the bank.
According to the Treasury Virgin has agreed that there will be no further compulsory redundancies, beyond those already announced, for at least three years from completion
It will have to retain and, over time, expand the total number of branches as well as loacate Virgin Money's HQ in Newcastle.
Support for the Northern Rock charitable foundation will also be extended for a further year.
George Osborne said: "The sale of Northern Rock to Virgin Money is an important first step in getting the British taxpayer out of the business of owning banks."
He said it was "a good thing for the British high street and a good thing for the north-east of England"
The sale is expected to be completed on 1 January 2012.