LBi, which won the account after a pitch, has been appointed to work on "the online customer journey" with a special focus on redesigning Cunard Line's website for all three markets.
The agency will also create an optimised tablet experience to boost online bookings.
Cunard Line is a sub-brand of Carnival Group, which appointed Karmarama to its £6 million Carnival Cruises UK ad account in January.
Vizeum has handled media for Cunard Line since 2008, when it was appointed to the brand along with the sister Carnival brands P&O Cruises and Princess Cruises. Vizeum is unaffected by the review.
Claire Hazle, the head of digital marketing for Carnival UK, said: "We chose LBi because their response to our brief showed a real understanding of the brand and how the Cunard experience can be reflected in digital channels."Follow @KatherinePLevy