Engine problems struck The Norwegian Starr on Friday morning after leaving port and ruining holiday plans for more than 2000 travellers, forcing it to bob without direction 30km off the coast of Melbourne.
The ship was slowly towed to Port Philip Bay, Melbourne harbour by tugs on Saturday evening, and moored in the early hours of Sunday morning.
A new departure date is expected to be known within the next 24 to 48 hours but passengers were preparing to wait up to five days for the ship to be repaired.
"All guests are welcome to stay onboard while the ship is docked and then continue onto Auckland on the revised itinerary once the repairs are complete," the cruise line said in a statement.
"We expect the itinerary that commences in Auckland on February 18 to operate as originally scheduled."
Sources said that ship's second azipod failed last week after continuing issues with its other azipod, which started three weeks ago, causing the 16 year old vessel to sail at very slow speeds from Asia to Australia.
The company has apologised for the inconvenience and given all guests a full refund and 50 percent future cruise credit.