The Carnival Triumph was towed into the port in Mobile, Alabama, amid cheers after more than 4,200 people spent an extra three days on a filthy, disabled ship.
Once the ship was tied up at the dock, getting all the passengers off was expected to take four or five hours, said Carnival Cruise Lines Vice President Terry Thornton.
The company said 100 motor coaches were available for passengers who asked to be taken back to Galveston, Texas, where the cruise started.
The Triumph was on its way home Sunday when a fire left the vessel drifting in Gulf of Mexico currents.
Follow complete coverage of breaking news on CNN TV, http://cnn.com and CNN Mobile. Watch a live update from Carnival officials momentarily.
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