They are now urgently trying to trace people who came into contact with them during their stay.
On Wednesday night, the Staycity Hotel on Paragon Street, near York Barbican, was put on lockdown when a man, understood to be a Chinese national, was taken to hospital after falling ill.
Witnesses saw paramedics wearing quarantine suits treat him at around 8pm.
The pair are being treated by Newcastle upon Tyne Hospitals NHS Foundation Trust in its specialist Airborne High Consequences Infectious Disease Centre (HCID).
It is understood that they travelled to the UK from China recently and are undergoing treatment at the Newcastle Royal Victoria Infirmary.
Prof Sharon Peacock, Director of the National Infection Service, Public Health England, said on Friday: “Public Health England is contacting people who had close contact with the confirmed cases.
"The two cases were staying in York when they became unwell.
"Close contacts will be given health advice about symptoms and emergency contact details to use if they become unwell in the 14 days after contact with the confirmed cases.
“This tried and tested method will ensure we are able to minimise any risk to them and the wider public.”
Earlier, Prof Peacock said that while staff are working to trace people who have been in contact with the pair, they do not currently have "any idea" of how high that number might be.
Staycity Aparthotels York has also confirmed two guests staying in their hotel have tested positive for coronavirus.
A spokesperson said: "We have now received confirmation that two guests staying in one of our apartments in York have been tested positive for the coronavirus.
"We have been advised by Public Health England that there is minimal ongoing risk of infection to either guests or staff, and as such our York property remains open for business.
"In due course the apartment concerned will undergo a thorough environmental clean and disinfection by a specialist contractor.
"We would like to reassure all our guests that we are following official advice on this matter and that the health and safety of everyone working and staying in our properties remains of paramount importance to us."