Virgin Money is to buy Northern Rock for an initial outlay of £747 million.
The sale is expected to complete by the end of the year, with the potential in the future to receive over one billion pounds in total, Northern Rock said.
The operational headquarters of the combined business will be based in Newcastle.
Virgin Money has committed to no further compulsory redundancies beyond those already announced by Northern Rock, for at least three years.
The total number of Northern Rock branches will be retained and extended in due course as business growth allows, virgin said.
The addition of Northern Rock to the existing Virgin Money business will create a group with over four million customers and a nationwide network of branches. The combined business will provide savings, mortgages, current accounts and credit cards, as well as insurance and investment products.
Ron Sandler, executive chairman of Northern Rock plc, said: “The return of Northern Rock to the private sector has always been one of our key objectives. We said that this would be done at the right time and when there was a proposition in the best interests of taxpayers and other stakeholders. I am delighted that we have reached an agreement with Virgin Money which successfully delivers that.