Switzerland’s Union Bancaire Privee will buy the private banking and wealth management business for a reported fee of up to £580m.
A spokeswoman for Coutts International said neither party would disclose the price of the deal, although the private banking business is tipped to have a £400m to £580m price tag.
RBS, which is 80 per cent owned by the taxpayer after being bailed out during the financial crisis, will keep hold of the UK operations of Coutts, which numbers the monarch among its clients.
The international arm of Coutts held £22bn in assets at the end of December, and manages clients from offices in Switzerland, Monaco, UAE, Qatar, Singapore and Hong Kong.
RBS said the sale would result in a £200m hit to its first quarter results after taking into account restructuring and other char- ges.
It added that it expects most of the sale to be completed in the final quarter of this year when the majority of the business is expected to transfer, with the remainder moving during the first part of 2016.
Alison Rose, chief executive of commercial and private banking at RBS, said: “Last year we set out a clear strategy to create a truly UK-focused bank. This announcement is another important step in that process.
“Following an extensive review, it was clear that the bank we are building would not be the most appropriate owner of the business being sold.”
Earlier this week, RBS announced the sale of up to £2.5bn in shares in US bank Citizens, reducing its stake in the bank to as little as 42 per cent.
RBS floated Citizens on the New York Stock Exchange in September 2014, as part of its plan to sell out of the business by the end of 2016.