A spokesperson for York Teaching Hospital NHS Foundation Trust, which runs the hospital, said: "Sadly, we can confirm that a patient being cared for at Scarborough Hospital, who had tested positive for Covid-19, has died.
"Our thoughts and condolences are with their family at this difficult and distressing time."
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The news comes after the first cases of the virus in Scarborough Hospital were confirmed on Monday.
As of 5.00pm on Thursday (March 26), there are 11,658 confirmed cases in the UK, of which 50 are in North Yorkshire and 14 in York.
In the UK there have been 578 deaths.
As York and North Yorkshire have separate unitary authorities they are classed as separate areas.
There are also 21 confirmed cases in the East Riding of Yorkshire.
The total across the whole of Yorkshire has now surpassed 550.
Yesterday Scarborough Hall Care home confirmed a resident had tested positive for Covid-19.
A spokesman for Barchester Healthcare - which runs the home - said: “We can confirm that we have had a positive test result for COVID-19.
"We are confident in the processes in our home with all of our staff trained in infection control, and our staff have been brilliant in implementing this.