The 3,660-guest ship, build by Fincantieri in Italy, is Princess’s sixth and final of its class, joining sisters Enchanted Princess, Sky Princess, Majestic Princess, Regal Princess and Royal Princess in the Princess fleet.
A naming ceremony will be held for the ship in Los Angeles on 29 April.
Long-time Princess guests Michael and Sally Smith were the first to board the ship prior to its departure on Sunday (27 March).
John Padgett, Princess Cruises president, said: “Cruising is back, and the elegant Discovery Princess showcases the many reasons why travellers should take a cruise now. We also recognise and applaud the ship’s company, who will work tirelessly to deliver memorable cruise vacations to all who sail on this magnificent cruise ship.”
Princess will bring its MedallionClass offering to the UK this summer when Enchanted Princess homeports in Southampton, sailing – from 4 May – 13 new voyages ranging from four to 14 nights.
It will be joined by fellow MedallionClass ship Sky Princess in Southampton, along with Emerald Princess and Island Princess.
New itineraries include voyages to the Canary Islands, across the Mediterranean, Scandinavia, Norway and Iceland.