The Carnival Triumph docked in Mobile, Alabama, at 21:15 on Thursday.
Disembarking the passengers took more than four hours and many still face a long bus journey home or to the port of departure, Galveston.
Passengers had reported sewage on the floors, poor sanitation and access to toilets, and lengthy queues for food.
Some lined the decks as the 900-ft ship docked, waving and cheering at people on shore.
Chants of “Let me off, let me off!” could be heard coming from the ship as they waited to disembark.
One homemade sign read: “Sweet Home Alabama!” and another: “The ship’s afloat, so is the sewage.”
Disembarking passenger Brittany Ferguson said: “I’m feeling awesome just to see land and buildings. The scariest part was just not knowing when we’d get back.”
Carnival Corp which operates the ship, was also the owner of Costa Concordia, the cruise ship that ran aground off the Italian coast and sank last year, killing 32 people.
The Carnival Triumph took six hours to be towed through the 30-mile channel to the docks at Mobile – the largest ship ever to dock there.
The passengers are being taken by bus either to Galveston in Texas, which is about seven hours away, or to New Orleans, where the firm said it had booked 1,500 hotel rooms. New Orleans is two hours away.
Carnival CEO Gerry Cahill apologized again for the “very poor” conditions on board.
“We pride ourselves on providing our guests with a great vacation experience, and clearly we failed in this particular case,” he said.
Hospitality staff will be sent on early holiday with full pay or transferred to other ships, depending on the length remaining in their contracts, senior vice-president Terry Thornton said.
Passenger Janie Baker told NBC by phone on Thursday that conditions on the ship were “extremely terrible”. There was no electricity and few working toilets, she said.
Janie Baker described using plastic bags to go to the toilet and that she had seen a woman pass out while waiting for food.
The stench from overflowing toilets and drainpipes made some cabins uninhabitable and many people slept in corridors, while others took bedding out into the open to escape the heat and foul smell.
Passengers will be offered a full refund and discounts on future cruises. Carnival announced on Wednesday passengers would each get an additional $500 in compensation.
But the firm has disputed the accounts describing the ship as filthy, saying employees were doing everything they could to ensure people were comfortable.
Carnival has cancelled more than a dozen planned voyages aboard the Triumph, while acknowledging that the crippled ship had other mechanical problems in the weeks before the fire.
Spokesman Vance Gulliksen said Triumph had an earlier electrical problem with the ship’s alternator but that repairs were completed by February 2. He said there was no evidence linking the previous problem to Sunday’s fire.
The National Transportation Safety Board has opened an investigation into the fire.
No-one was injured in the blaze, but one passenger with a pre-existing medical condition was taken off the ship as a precaution.
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