Tim Harris, chairman of P&O Cruises, said the only British yard with the capacity to build the ship - Harland & Woolf in Belfast - had declined to quote for the contract.
He said the Italian yard had already built two ships for P&O to a very high standard.
The ship, if it were in commission now, would be the largest cruise liner in the world at 77,000 tons, 12,000 tons heavier than the QE2. But Carnival, P&O Cruises' US competitor, has a bigger one under order.
The P&O ship - Sun Princess - will have 1,950 berths, a 300-place conference centre and five dining areas. Among the features will be an 'ultra-deluxe' health centre.
P&O is one of the three big players in the cruise market, and the new liner will join a 14- strong fleet. It is due for delivery in December 1995 and is expected to enter service immediately with Princess Cruises, P&O's Los Angeles subsidiary.
Dan White, an analyst at NatWest Markets, said: 'We think this is a very good deal as P&O has got a good price because of the strength of the dollar and the weakness of the lira. The terms are also favourable as 80 per cent of the price does not have to be paid until delivery.' P&O shares jumped 13p to 533p.