The Costa Allegra, the wrecked Italian cruise ship, docked in the Indian Ocean islands in the Seychelles.
The Costa Allegra was towed to the main port of the islands, Victoria, by a French fishing boat.
There are more than 1,000 passengers on board and the evacuation is expected to take several hours.
Costa Allegra, which lost power on Monday, is from the same fleet as Costa Concordia, which capsized off the Italian coast in January, killing 32 people.
As the Costa Allegra has no power, it will take at least two hours to get the ship to the dock so that passengers can disembark.
Passengers who are in the weakest medical condition will be taken first.
Those on board spent three days without electricity or hot food, with supplies by helicopter.
The ship also does not have a functioning air conditioner. Most of the passengers stayed on deck to take advantage of the cooling breeze in hot weather.
Accommodation is being arranged, but for already occupied hotels most are expected to fly directly to Italy.
Planes are lined up in the Seychelles to take passengers home from the ship as soon as possible.
Costa Cruises, which owns Costa Allegra, says it received its regular dry dock maintenance in October 2011.