The new Voyager ships will be capable of carrying around 4,700 passengers versus its Sphere-class's capacity of 4,300, its current largest vessels.
The deal with Italian shipbuilder Fincantieri for the three new-builds will see deliveries begin in late 2035, with further deliveries in 2038 and 2039.
Princess said the Voyager ships would build on learnings from its Sphere-class vessels, bringing the latest guest-facing features and marine/propulsion technologies.
Notable features will include reimagined outer decks, staterooms and piazza designs, reflecting its global clientele and deployments.
Voyager ships will be dual-fuel, with power coming primarily from liquefied natural gas (LNG) offering lower emissions than conventional marine fuels. Each will be 183,000 gross tonnes.
Neither Fincantieri nor Princess, or its parent Carnival Corporation, disclosed the exact value of the order, which remains subject to financing and terms.
However, Fincantieri said the agreement was considered "very important", which it added typically reflected an order value in excess of €2 billion.
"Voyager class will delight both our loyal guests and attract the next generation of Princess guests," insisted Princess president Gus Antorcha.
"We have been leveraging extensive customer and agent research to strike the right balance between evolving our proven winners and introducing new concepts and partnerships grounded in what matters to our current and future guests.
"From exceptional dining and inviting pool environments to elevated entertainment and beautifully reimagined spaces throughout the ship, we are leaving no area untouched as we thoughtfully evolve the Princess experience."
The three new ships will become Carnival's 19th, 20th and 21st LNG-powered vessels. The group has another seven new ships scheduled for delivery between 2027 and 2033.
Pierroberto Folgiero, chief executive and managing director of Fincantieri, said: "These new orders secure a robust workload for our shipyards through 2039 and further support the profitable development of our cruise business.
"With the new Voyager-class ships, we are once again leveraging Fincantieri’s distinctive expertise in sustainable, next generation shipbuilding, supporting Princess Cruises in its growth trajectory and reaffirming our role as a trusted industrial partner for the evolution of the cruise industry."
