The value of the gross assets included in the sale was $2.7bn as of 31 October 2011.
HSBC said that the sale represents further progress in the execution of its strategy outlined at the investor day in May 2011.
The transaction, which is subject to regulatory approvals, is expected to close during the second quarter of 2012.
Financial terms of the deal were not disclosed.
In November 2011, Credit Suisse has revealed its plans to integrate Swiss private bank Clariden Leu in to its organization to achieve further growth and annually recurring cost savings of around CHF200m.
HSBC serves customers worldwide from around 7,500 offices in over 80 countries and territories in Europe, the Asia-Pacific region, North and Latin America, and the Middle East and Africa.
