One crew member performed an impromptu haka after disembarking the vessel on Tuesday, earning applause from those on board.
One woman from Ireland, meanwhile, said she was “absolutely delighted” and “never thought the day would come”.
“I’ve been in the cabin for like, about a month now,” she said in footage shared by NSW Police.
“It’s so surreal … it’s slightly overwhelming.”
At least 49 crew members from six countries were due to disembark the ship, which has been docked at Port Kembla for more than two weeks following a COVID-19 outbreak.
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NSW Police Commissioner Mick Fuller said the health and safety of crew and the wider community would remain the priority as the repatriation process began.
“The movement of the first crew contingent today is an important milestone, and has us one step closer to the Ruby Princess leaving Australian waters,” Mr Fuller said in a statement on Tuesday.
One crew member expected to leave the ship has tested positive for COVID-19 and will be taken to a NSW Health-managed hotel for 14 days of quarantine before returning home, according to police.
The remaining 48 crew have tested negative and arrangements are being made for flights to their home countries.
NSW Police says more crew members will disembark in coming days, but hundreds will remain on board and return with the ship to its port of origin.
Deputy Commissioner Gary Worboys said the ship was on track for a Thursday departure.
The Ruby Princess initially docked in Sydney in March, when the ship’s passengers and some crew disembarked.
It has since been linked to at least 21 deaths and hundreds of coronavirus cases across Australia.
Most of the crew have remained in isolation on the ship and 190 of those on board had tested positive for COVID-19 as of Sunday night.
Another 12 crew members infected with coronavirus have previously been evacuated to NSW hospitals.
NSW opposition leader Jodi McKay said the ship should stay on Australian shores until every crew member was either well or repatriated to their home countries.