At least 213 people in China have died from the virus, with almost 10,000 cases nationally.
There have been 98 cases in another 18 countries.
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Prof Chris Whitty, chief medical officer for England said the NHS was "extremely well-prepared for managing infections" and it was quickly trying to identify any contacts the patients had to prevent further spread.
He said the two people could not be identified because of patient confidentiality.
"We have been preparing for UK cases of novel coronavirus and we have robust infection control measures in place to respond immediately," he added.
'High chance of getting better'
Prof Whitty said the unit at the Royal Victoria Infirmary was experienced in treating people with infectious diseases and there was "a high chance people would get better", based on current information.
"A lot of people will end up with a relatively minor disease," he said.
The small number who go on to be more seriously ill tend to develop respiratory problems which "will be dealt with as anyone else with a respiratory disease," Prof Whitty added.
He indicated that efforts would now be made to trace everyone in close contact with the two coronavirus cases so they could be monitored.
Ian Jones, professor of virology at the University of Reading, said the possibility of further spread was "minimal" because the cases were caught early.
Virus experts said they were not surprised to see cases in the UK, but this was no reason to panic.
"This is still primarily a Chinese emergency as 99% of cases have been in China and all deaths have been in China," said Prof Devi Sridhar, from the University of Edinburgh.
The WHO declared the outbreak a global emergency on Thursday.
The number of coronavirus cases worldwide has now surpassed that of the Sars epidemic, which spread to more than two dozen countries in 2003.
The mortality rate for the new strain of coronavirus is currently low, at 2% - less than Sars at 10% and Ebola at 70%, the chief medical officer says.
But the death rate could yet go up if more of those in hospital die, or down if it's discovered there are many other people with mild symptoms.