Union Bancaire Privee (UBP) has agreed to buy Royal Bank of Scotland's international private banking business Coutts International, as the Swiss private bank continues to rebuild its asset base in the aftermath of the financial crisis.

Geneva-based UBP said the purchase includes the business managed from Switzerland, Monaco, the Middle East, Singapore and Hong Kong, and assets under management of over 30 billion Swiss francs ($31.02 billion).

UBP Chief Executive Guy de Picciotto described the deal as a "significant milestone" in the bank's growth strategy.

"This is particularly true for high-potential markets such as Asia, where the international business of Coutts has built long-standing relationships with high net worth clients," de Picciotto said in a statement on Friday.

For UBP, this is its first major deal since it bought Lloyds Banking Group's international private banking arm in May 2013, and is another step in rebuilding its asset base which almost halved through the financial crisis.

UBP had 98.7 billion francs in assets under management at the end of 2014 compared to its peak of 135 billion francs in 2007.

A spokeswoman for Coutts International said neither party would disclose the price of the deal.

RBS said the sale price will be determined by the assets under management when the sale concludes, adding that it will be a premium to the book value of the business.

The British bank also said the deal would include 15,000 to 20,000 customers, though RBS will keep about 3,000 international clients who have close links to Britain.

Britain's Financial Times reported on Thursday UBP is expected to pay about $600 million to $800 million, citing two people familiar with the situation.

A source had told Reuters the range reported was accurate but declined to give further details.

It is another step by RBS, 80 percent owned by the UK taxpayer, to pull back from international markets and focus on core UK retail and commercial banking.

It said the capital benefit from the deal would be modest after it writes off goodwill related to the business and after exit and restructuring costs.

There will be a charge of about 200 million pounds ($296 million) in its first quarter results, primarily due to the goodwill write off.