RBS' privatisation will cost the British taxpayer around £7 billion
Osborne said that a "decision point" had been reached and the Governor of the Bank of England Mark Carney said the sell-off "would promote financial stability" and benefit the wider economy.
"It's the right thing to do for British businesses and British taxpayers," said Osborne in his speech last night. "Yes, we may get a lower price than that was paid for it - but we will get the best price possible. For the longer we wait, the higher the price the whole economy will pay."
Around seven years ago, RBS had to beg the government for a bailout. Over 2008 and 2009 it borrowed £45.4 billion ($70.1 billion), worth 500p per share, from the taxpayer and it has yet to pay it back. The government still owns 81% of RBS.
If the government sold RBS off right now, it would be at a major loss, as the share price was around 354.8p when the announcement was made.
This morning, however, it looks like investors are happy with the decision and shares are rising around 2% in the market open.
"I welcome this evening's announcement from the Chancellor and we are pushing ahead with our strategy to build a simpler, stronger, fairer bank that is totally focused on the needs of its customers and centred here in the UK," said RBS's chief executive, Ross McEwan, in an emailed statement. "When the Government starts selling its shareholding, it will be selling a bank determined to be the best in the country."
Here is Osborne's full speech from Mansion House last night: