UK Government Investments (UKGI) confirmed the “successful completion” of the disposal at a placement price of 271p per share.
The sale of around 925 million shares will bring the public holding in RBS down from approximately 70.1% to 62.4%, resulting in proceeds of £2.5 billion.
It comes at a £2.1 billion loss to the UK taxpayer, with the Government having paid an average of 502p per share during its bailout of RBS during the financial crisis.
That loss is expected to balloon to around £26.2 billion as the Government hopes to have sold off around two thirds of its stake by 2023.
The Government bought its stake in the bank for £45 billion in 2008 as part of a bailout at the height of the financial crisis.
This week’s share sale is the first time that Government’s holdings in RBS have been offloaded since 2015.
RBS chief executive Ross McEwan said: “I am pleased that the Government has decided the time is now right to restart the share sale process.
“This is an important moment for RBS and an important step in returning the bank to private ownership.
“It also reflects the progress we have made in building a much simpler, safer bank that is focused on delivering for its customers and its shareholders.”