LONDON—The U.K. government on Tuesday said it had sold a 5.4% stake in Royal Bank of Scotland Group PLC, raising £ 2.08 billion ($3.24 billion) and kicking off a long-awaited privatization of the lender.

UK Financial Investments Ltd., the body that manages the government's bank shareholdings, said it had sold the shares at 330 pence each, representing a 2.25% discount to the bank's closing share price on Monday.

The issue was 2.4 times oversubscribed, with the majority of buyers being short-term investors, according to a person familiar with the matter. The U.K. said Monday it planned to start selling its stake in RBS via an overnight book build.

Shares in RBS fell 1.7% in early trading in London.

Following the sale, the U.K. Treasury's economic interest in RBS, which includes its holding of ordinary shares and B shares in the company, will be reduced to 72.9%. It has agreed not to sell any more shares for 90 days.

RBS Chief Executive Ross McEwan welcomed the sale of the shares, which the government acquired when it bailed out the bank in 2008.

"It's an important moment and reflects the progress we are making to become a stronger, simpler and fairer bank. There is more work to be done but we're determined to build a bank the country can be proud of," Mr. McEwan said.

The U.K. government pumped in £ 45.5 billion to rescue RBS during the financial crisis at an average price of £ 5 a share, meaning the British taxpayer will lose money from the share sale.

U.K. Chancellor George Osborne said the sale was the right thing to do for the British economy.

"I wasn't the Chancellor who bailed out RBS; but I am the Chancellor now responsible for doing the right thing for the British economy," Mr. Osborne said. "So while the easiest thing to do would be to duck the difficult decisions and leave RBS in state hands; the right thing to do for the economy and for taxpayers is to start selling off our stake."

Following the 2008 bailout government officials hoped RBS's vast international and investment banking operations would help generate enough profit to put the bank on its feet. However by 2013 the losses were still mounting and it became clear the government's hands-off strategy had failed. The U.K. government became more proactive, ousting RBS's chief executive, forcing the bank to chop down its investment bank and divest its U.S. operations.

U.K. officials gave up on the idea that the bank's shares would soon rise above the original bailout price.

Earlier this year the Treasury was advised by UKFI that it would be feasible to sell  £ 25 billion of RBS shares by 2020, effectively firing the starting gun on the sale.

It is unclear what returns U.K. taxpayers will make on the money locked up in RBS. The bank is currently going through a vast restructuring, which isn't set to be completed before 2019. Last week RBS warned that it wouldn't be paying dividends until at least the start of 2017 as it looks to hurdle balance sheet stress tests and settle many litigation issues.

Write to Max Colchester at max.colchester@wsj.com and Ian Walker at ian.walker@wsj.com

Subscribe to WSJ: http://online.wsj.com?mod=djnwires