The vessel was slated for delivery in 2010 and the contract was worth some 410 million euros (547 million dollars).
The MSC Magnifica is the fourth in its class and can carry up to 4,000 people including crew, the group said.
Aker Yards builds cruise vessels, ferries, merchant vessels, offshore and specialized vessels.
Aker Yards has some 20,000 employees and operates 17 shipyards in Brazil, Finland, France, Germany, Norway, Romania and Ukraine. It is also building a shipyard in Vietnam for offshore and specialized vessels.