Rosselli will be London-based and report to managing director and head of TWS Steve Griffiths, who joined Coutts in May also from Credit Suisse.
He will be responsible for the leadership and development of the TWS international teams focusing on markets in Asia, Russia and the Middle East.
Rosselli will also lead on enhancing the products and solutions suite and reviewing how they are delivered to clients.
At Credit Suisse Rosselli has most recently been head of wealth planning and prior to this he held a number of wealth planning roles at UBS, both in Switzerland and the UK.
Griffiths said: "Tax & Wealth Structuring is a key area of development for Coutts, especially as our clients’ requirements in tax, fiduciary & estate planning become increasingly important. Armando’s appointment is a milestone in building the TWS global strategy and he will work very closely with me in developing and executing this.
"This further demonstrates our continued growth plans and complements the recent hires in the products and services team, both in the UK and Asia. Providing our clients with exceptional wealth management that meet their evolving needs is a key driver in our strategy for growth."