The older patient had been "in an out of hospital" for other reasons but was admitted on Wednesday evening to the Royal Berkshire Hospital and tested positive.
The news comes as cases of coronavirus in the UK have more than doubled in 48 hours as the country moves towards the "delay phase" of tackling the virus.
Some 116 people have tested positive, including 105 in England, two in Wales, six in Scotland and three in Northern Ireland.
Just two days ago there were 51 UK cases.
A statement from the Royal Berkshire NHS Trust said: "Sadly, we can confirm that an older patient with underlying health conditions has died.
"The patient has previously been in and out of hospital for non-coronavirus reasons, but on this occasion was admitted and last night tested positive for coronavirus.
"The family has been informed and our thoughts are with them at this difficult time."
England's Chief Medical Officer, Professor Chris Whitty, said he was "very sorry" to report the news and offered "sincere condolences" to the family.
He added: "The patient, who was being treated at the Royal Berkshire Hospital, was an older patient who had underlying health conditions.
"We believe they contracted the virus in the UK and contact tracing is already underway."
Last week, the Foreign Office confirmed a British tourist who had been on board the Diamond Princess cruise ship, which was quarantined in Japan, had died from the virus.
Downing Street on Thursday said it is "highly likely" that coronavirus will now spread in a "significant way".
Earlier, Prof Whitty warned that critical care beds in the NHS could come under intense pressure during a coronavirus epidemic.
Of the new cases, 17 people had recently travelled from countries or clusters already under investigation, while eight people contracted the virus in the UK and are being investigated.
Out of the cases identified in England, 25 of them are in London.
The North West and South East each have 17 cases, the South West 15, the East of England eight, the Midlands nine and the North East and Yorkshire 10 cases.
Four other cases are still to be determined.
Local regions reported that two new cases were in Staffordshire, one was linked to the University of Sussex in Brighton, two were in Wigan, one in Rotherham, two in Liverpool, and one in Birmingham.
In other key developments:
- ITV revealed that travel companies are deferring their TV advertising because of the disease, with advertising revenue due to drop 10% in April.
- The Grand Princess cruise ship, with around 2,500 passengers and 1,000 crew, is being held off the coast of California after a former passenger died from Covid-19.
- Starbucks said it was "pausing the use of personal cups" and washable ceramic cups for those drinking their beverage in US and Canadian stores due to coronavirus fears.
- England's Six Nations rugby match against Italy on March 14 in Rome has been postponed due to the coronavirus outbreak.
- A statement from HSBC said one of its employees at Canary Wharf had been infected.
Prof Whitty gave evidence to the Health and Social Care Committee, with MPs including former health secretary Jeremy Hunt.
He said it would be "lucky" to get a vaccine for Covid-19 in the next year, but it would "not get us out of a hole now", although other treatments may work.
Prof Whitty acknowledged that people needing oxygen would stretch the health service, and said some "things may be considerably less well done" during the peak of an epidemic.
He pointed to potential stress on the service at the worst point, adding: "Depending on how high the peak, this could be anywhere from a rather bad winter for the NHS - but in spring or summer - through to huge numbers way overtopping the ability of the NHS realistically to put everyone in beds and that obviously would have big pressures on the service."
Half of all coronavirus cases in the UK are most likely to occur in just a three-week period, with 95% of them over a nine-week period, he said.
In a worst-case scenario, "the ratio of doctors to patients and nurses to patients would inevitably go down very sharply for a short period of time", he said, but said the NHS is "incredibly good at flexing" to meet demands.
He added: "The bit of the system which will come under pressure first will be those conditions that require people to have oxygen and particularly to have critical care beds, and that bit, I think, will come under pressure at quite an early stage if we have a high-end-of-the-range epidemic for this."
Prof Whitty said he had a "reasonably high degree of confidence" that 1% is at the "upper limit" of the mortality rate for coronavirus, although Wuhan in China, which has a weaker health system, had seen an 8% to 9% mortality rate for those aged 80 and over.
He said the UK has now mainly moved to the delay stage of tackling the virus, where measures can be ramped up to delay its spread.
Possibilities include school closures, encouraging greater home working, and reducing the number of large-scale gatherings.
However, Prof Whitty said closing schools would possibly only have a "marginal effect", adding that children do not appear to be as badly affected by Covid-19 as other groups.
Meanwhile, Prime Minister Boris Johnson sought to reassure the public on ITV's This Morning, saying it would be "business as usual" for the "overwhelming majority" of people in the UK.
"People can see that this country is going to get through this in good shape," he said.
Prof Whitty said elderly people should not self-isolate yet, and neither should those with conditions such as asthma, adding there was no evidence of "deep harm" in children with asthma.
And he said pregnant women should not start worrying about coronavirus, but advised any smoker to stop.
Symptoms of Covid-19 appear around five days after infection, he said. It then takes up to a week to recover, with the serious illness setting in for some after six days.