In a post on Facebook, David and Sally Abel said they had been taken off the Diamond Princess on Thursday and were now undergoing a series of tests.
David added: “Outside the hospital I came over a bit weird and nearly passed out. Every pore on my body opened and i was wheel-chaired to our room.
“Full health inspection and now we know what’s going on. We both contracted a cold (unaware of) and it has not yet turned into pneumonia. (We do have coronavirus).”
The couple were taken off the cruise ship after confusion over whether or not they had actually contracted the virus.
The couple have been posting regular updates on social media about their situation and on Tuesday announced they had been told they had contracted coronavirus but did not have any symptoms.
Later that day they posted on Facebook suggesting there had been a “massive communication error” with Japanese officials and that they might not have coronavirus after all.
The Diamond Princess was quarantined in the port of Yokohama on 4 February for two weeks after a man who left the ship in Hong Kong was later diagnosed with the virus.
Two other elderly passengers taken off the ship because they were infected with coronavirus have died, Japan’s Health Ministry said on Thursday.
They are the first fatalities from the virus-stricken boat, and Japan now has three deaths linked to the Covid-19 illness.
Japan’s NHK public television said both were Japanese and in their 80s. A Health Ministry official only confirmed that they had been previously taken to hospital in serious condition and had existing chronic diseases.
More than 540 people have tested positive for Covid-19 on the cruise, which originally carried 3,700 passengers and crew, with those infected transferred to hospitals in Japan.
Other Brits aboard the ship are due to be evacuated on Friday via a flight from Tokyo.
Foreign secretary Dominic Raab said information has been provided to those registered for the flight, but he urged “other British nationals still seeking to leave to contact us”.
He added: “We will continue to support British nationals who wish to stay in Japan.”
There were 78 British passengers on the cruise liner when cases of the coronavirus strain known as Covid-19 started to emerge.
Four British cases have since been confirmed by the Foreign Office.
It is understood only healthy passengers with no symptoms of the virus will have a seat on the plane, with all to spend 14 days at the Wirral.
Anyone who develops symptoms during the flight will be taken to hospital, while it is understood any pre-existing cases will be treated in Japan.