Tina tested positive for Covid-19 but has been symptom-free 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.
Tina said their departure from Uruguay was "pretty special".
Locals waved flags at their buses as they were driven to the airport.
"We could see people standing on the roadway, in doorways on balconies, waving. There were people waving flags," Graham said.
"It was incredible. We had obviously been on the news there and they had a rough idea, but people were literally standing out waiting for us to come through - so that was a really wonderful sight."
Those who had tested positive for the virus were put onto different buses to those who were negative.
Then the buses were escorted to the airport via roadblocks.
"We had between six and eight motorcycles in front of us with police cars, flashing lights, sirens the whole way," Graham said.
"Then we had just an ordinary car with hazards lights on, then our bus, then there were police cars or an ambulance between each of the buses."
News crews were filming along the way, photographers were on board the pilot boat that directed the cruise ship to dock at Montevideo and a drone with a camera was in the air.
A chartered medevac flight carrying them and 11 other New Zealanders arrived at Auckland Airport yesterday afternoon, from Melbourne.
They left Uruguay last week on a flight to Australia, with 96 Australians who had also been on the cruise.
Three New Zealanders remained in Australia, where they normally live.
Tina and Graham left New Zealand on March 11 and their cruise left Argentina, headed to Antarctica and South Georgia, on March 15.
Graham watched "four-and-a-half movies" on the plane to Melbourne, while separated from Tina.
The Kiwis taking the second flight to Auckland were questioned in Melbourne and had their temperatures taken before they could board the next plane.
"It was a real privilege to be able to fly into Australia and have the opportunity to fly home. We were all watching the NZ coastline as it approached ... We had a very nice flight home," Graham said.
"People were clapping [when landing], a lady next to me was a little bit emotional. Everyone's been very friendly and helpful which has made our arrival much easier to handle. We are very grateful to be home."
In their motel in Auckland, the pair were swabbed again for Covid-19 and their temperatures, heart rate and blood pressure was taken again by nurses.
Police and security have also made a presence at the hotel.
Their stay for quarantining is being paid for by the New Zealand Government.
Aurora Expeditions paid for the flight to Australia, and the couple paid for their flight to Auckland but are likely to be reimbursed by the cruise company for this.
A media statement from Aurora Expeditions yesterday afternoon said the company was "thrilled" to have brought the New Zealanders and Australians home.
"We thank them for their patience as we navigated this challenging situation."
"We are incredibly grateful for the support and care offered by the Uruguayan government and health workers throughout this process," it said.
"We remain in touch and focused on supporting the two passengers and their families who remain in hospital in Uruguay. They are receiving the very best of care ... We continue to remain 100 per cent focused on getting the remainder of our passengers back to their home nations as soon as we can."