Some 57 crew members on Tuesday disembarked the ship and travelled to New South Wales hotels to be repatriated over the next three days on charter flights.
They will be isolated in their hotel rooms until their flight.
The ship returned to Sydney after a New Zealand trip that included stops in several ports, including Dunedin and Akaroa.
NSW Police Commissioner Mick Fuller on Wednesday told reporters Australian Border Force Commissioner Michael Outram had written to cruise ship parent company Carnival Australia and directed the Ruby Princess to depart national waters on Thursday.
However, some 40 crew members on board the Ruby Princess remain particularly ill with Covid-19 and NSW Health is monitoring the situation.
The ship's captain was coronavirus-free and able to sail the vessel.
"Nine individuals flew home last night, another 18 (are) flying home today and the rest will fly home over the next two days," Mr Fuller said.
"It was either the responsibility of Carnival or the individual consulates to arrange transportation home - that was the deal I cut."
The Australian Border Force has been contacted for comment.
Crew members on Tuesday clapped and cheered from their balconies as the first of their workmates finally began to disembark.
Hundreds of others will remain on board for the ship's journey to its home port.
One disembarking female crew member 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."
The Ruby Princess initially docked in Sydney in March when the ship's 2700 passengers disembarked without adequate health checks. It has since been linked to at least 21 deaths and hundreds of coronavirus cases across Australia, where the death toll was 74 on Wednesday.
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 this week said the ship should stay on Australian shores until every crew member was either well or repatriated to their home countries.
A NSW criminal investigation into the Ruby Princess cruise ship debacle is likely to be made public when it reports back in September.
A special commission of inquiry overseen by barrister Bret Walker SC is running in parallel to the police probe, while a coronial inquest remains a possibility.
