The firm is the first taxpayer-owned bank to be returned to the private sector.

Northern Rock was nationalised in February 2008, split into two companies Northern Rock plc and Northern Rock (Asset Management) and Northern Rock plc was put up for sale in June.

The bank currently employs 2,500 people and Virgin Money has agreed to no redundancies for at least three years and no branch closures.

The Government will receive £747m in cash on closure of the deal and a further £50m within six months of completion.

However, taxpayers will end up with a loss of between £400m and £650m as the Government has spent almost £1.4bn on the firm.

Chancellor 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. It represents value for money, will increase choice on the high street for customers and safeguards jobs in the North East.”

Ron Sandler, executive chairman of Northern Rock plc, said: “Today’s announcement demonstrates the enormous progress that has been made at Northern Rock, which is a great testimony to the commitment and spirit of the people who work here.

“These are qualities that can be carried forward into the new business and help ensure a strong player will emerge to enhance competition and customer choice in high street banking.”

The sale is expected to be completed on 1 January.