The purchase, which leaves taxpayers facing a £400 million loss, creates a bank with four million customers and accelerates Virgin’s ambitions to take on the big five lenders.
The firm’s Edinburgh-based chief executive Jayne-Anne Gadhia, who will run the enlarged bank, said: “We think we would be ready for a flotation in two years and then it’s all down to the markets.
“It makes complete sense for us to be able to access capital markets if we are going to be a really significant player.”
Northern Rock has been in public ownership since February 2008, when it was at the centre of the first run on a UK bank in 150 years.
Chancellor George Osborne insisted the price was the best available.