Both the MS Zaandam and MS Rotterdam have docked in Port Everglades, Florida, after weeks at sea.
The Holland America Line vessels, which have been hard hit by the coronavirus pandemic, arrived following the intervention of United States president Donald Trump.
A British man was among four people who died on Zaandam.
The vessel was carrying hundreds passengers when it set off a South America cruise from Buenos Aires to San Antonio on March 7th.
Failed attempts were made to disembark guests in Chile on March 15th and at other ports along its route to the United States, before eventual arrival in Florida.
A total of 107 passengers – 90 on Zaandam and 17 on Rotterdam – and 143 crew on Zaandam have presented with influenza-like symptoms since March 22nd.
The situation is thought to have deteriorated further in the interim.
Passengers fit to travel amid guidelines from the US centres for disease control and prevention were allowed off the ships in Florida after clearance was agreed with authorities.
They will be health screened and also cleared for entry by US customs and border protection.
Holland American Line president, Orlando Ashford, said: “These travellers could have been any one of us or our families, unexpectedly caught in the middle of this unprecedented closure of global borders that happened in a matter of days and without warning.
“We are so happy to be able to get our guests home and assist those few who need additional medical services.
“The Covid-19 situation is one of the most urgent tests of our shared humanity, and we must do everything we can to ensure we continue to act in ways consistent with our common human dignity.”
Disembarkation is expected to be completed by Friday evening local time.
Those deemed fit to travel will transfer directly to the airport to fly home, the majority on charter flights.
Passengers have not left the ship since March 14th and have self-isolated in their cabins since March 22nd.
Those who still have symptoms will remain on board and disembark at a later date to be finalised after they have fully recovered.
Coral Princess is now hoping to enter Port Everglades in Fort Lauderdale over the weekend.
For all the latest from Breaking Travel News on the coronavirus pandemic, take a look here.
Image: SMG/Zuma Press/PA Images