A charted medevac flight carrying them and 11 other New Zealanders arrived at Auckland Airport this afternoon, from Melbourne.
They left Uruguay on Friday night [NZT] on a flight to Australia, with 96 Australians who had also been on the cruise.
Tina tested positive for Covid-19 and, although Graham did not get a positive test, health officials believed he probably had the virus and recovered before testing began on the cruise.
Their son Ben told NZME this morning his family was "very relieved" his parents were on flights home.
"They [wider family members] were surprised ... by how bad the situation was there."
His parents were glad to "finally get moving" he said, and his children were looking forward to seeing their grandparents after they finish two weeks in quarantine.
He said the Uruguayan Government had been "fantastic" in helping the cruise passengers.
"I think everyone's done the best they can in the situation. No one, a few months ago, would have predicted where we are."
Tina and Graham, who NZME has agreed not to fully name, had planned a three-week voyage to Antarctica and South Georgia but that was cut short by fever on board and trouble finding somewhere to anchor last month.
They left New Zealand on March 11 and their cruise left Argentina on March 15.
They were told of the first fever on board on March 22 and went into lockdown onboard the Aurora Expeditions cruise, with food delivered to their rooms.
Graham's brother Ross said the couple would be "incredibly relieved" and "absolutely delighted" to get back on New Zealand soil.
He gave a "massive thanks to all those who knitted this repatriation flight together to get them back home".
"The situation has just dragged and dragged and dragged. We have been highly concerned for our family. It has been a very stressful time in their lives."
In a statement last night, Minister for Foreign Affairs Winston Peters said the New Zealanders on board were "in a position of real risk, where they were unable to shelter safely on the ship and were not in a position to return home via commercial means".
"Their imminent return to New Zealand is a seriously welcome result."
As a large proportion of passengers on the Greg Mortimer tested positive for Covid-19, all passengers were being treated as though they were Covid-positive as a precautionary measure, he said.
"A considerable amount of work has been put in to assist all 16 New Zealanders, who were in a dangerous situation with very limited options.
"We are deeply appreciative of the assistance we have received from Aurora Expeditions, and the Governments of Uruguay and Australia, in making this repatriation flight possible.
"Consular officials are navigating extremely complex circumstances every day, to find solutions that work, though Government chartered flights cannot be relied upon in a great many locations.
"Our advice to New Zealanders overseas remains to shelter safely where you are, or return home by commercial means.
"We are also working with our partners wherever we can to help people whose plans to return to New Zealand have been thwarted" Peters said.
In a media release this morning, National's spokesperson for Foreign Affairs Gerry Brownlee said New Zealanders stranded in India needed help to get home, too.
"We have Kiwis who are in India who are running the risk of being without medication, money and being evicted from hotels.
"India has had growing unrest since issue of their curfew. There has been an increase in crime and violence which is making an already worrying situation that much worse."
He said the ministry's advice to "shelter in place" "provides no practical help".
Director-General of Health Ashley Bloomfield said none of the New Zealanders coming back from Uruguay needed hospital care.
All passengers will enter immediate quarantine now they have been repatriated.
A New Zealand Defence Force C-130 Hercules carrying 39 people from Vanuatu also arrived in New Zealand today.
"The deployment of the C-130 to Vanuatu carrying a helicopter and additional supplies to support the Tropical Cyclone Harold response effort gave us the opportunity to repatriate a large group of New Zealanders seeking to return home," Winston Peters said in a press release.