Iona, named after the Inner Hebridean island, will join the P&O fleet in May 2020.
More than 30,000 people last year put forward names for the new 180,000-ton ship.
Paul Ludlow, P&O Cruises senior vice-president, said: “We are an island nation and as Britain’s favourite cruise line, it seems very fitting to highlight one of our most notable islands and celebrate the geographic diversity of the UK, especially as we can trace back our roots to the Scottish Isles.
“Iona played a significant part in shaping the history of our nation and we hope with this very special name our new ship will shape the future of holidays at sea for generations.”
Two sea crossings are still required to reach the island, sustaining trade and tourism routes.
Ludlow said this dependence on the sea informed a number of the line’s design choices to highlight its beauty.
“Iona is known for its peace and tranquillity, stunning landscape and, most importantly, the view of the ocean from almost every point on the island,” added Ludlow. This mirrors our primary intention when building the ship, which was to make the sea the star.
“Throughout the design process, we were mindful we were building a ship, not a hotel, and the intrinsic beauty of the sea, the vistas of the coastlines and ports of call should be at the fore and visible as much as possible from all areas of the ship.“
The name was unveiled by TV presenter Stephen Mulhern on Iona, where he was joined by several of islanders.
Holidays aboard Iona will go on sale in September, with further details of the ship, its design and itineraries to be released in the coming months.