The storm, which dissipated Sunday, delayed arrival by a day for the Carnival Elation and less than half a day for the Carnival Conquest, which had to remain in the Gulf of Mexico until the Coast Guard reopened the mouth of the Mississippi River about 12:15 a.m. Sunday.
"Our top priority was to keep a safe distance from the storm while we waited for the river to re-open," said cruise line president and CEO Gerry Cahill.
The Conquest was expected to reach New Orleans at 1:30 p.m. Sunday, and the Elation at 2 p.m., the company said in a news release.
Passengers who chose not to leave Sunday could stay on the ships until Monday morning.
Elation had 2,447, passengers, and Conquest had 3,274.
Both ships were to leave Monday on shortened cruises — the Elation's cut from five to three days and the Conquest's from seven to six, and from three stops to two.
Passengers who go on the Elation's cruise will get a 50 percent refund and a 50 percent discount toward a future three to five-day cruise. The Conquest's passengers will get a one-day refund.
Carnival has worked to restore passengers' confidence since the Carnival Triumph broke down in February, stranding passengers for five days in the Gulf.