The news follows the announcement last month that Paul Ludlow was leaving to join P&O Cruises.
Roberts, 40, has worked for Carnival UK for the past 15 years, most recently as director of technology partnering.
Jan Swartz, president at Princess Cruises, said: “I am delighted to appoint Tony to this pivotal role for Princess Cruises. His wealth of experience, including delivering successful projects in partnership with a wide range of stakeholders, means he is ideally placed to lead us in the UK and in Europe.”
Tony Roberts said: “It is an honour to be appointed to such a prestigious role, particularly as Princess is thriving in the UK and Europe markets. I will make certain we continue to succeed at every level, as well as ensuring that our guests’ experience is second-to-none from the moment they decide to travel with Princess. I look forward to working with the Princess teams across the globe as well as with those in Carnival UK.”