The prime minister wants the NHS to be “battle ready”, a No 10 spokesperson said.
The money will be available immediately and will be used in part to free up space in the NHS by paying private hospitals and maintaining the hastily built Nightingale hospitals until the end of March.
At a press conference in Downing Street, Mr Johnson is also due to publish a new section of the the government’s “road map” out of lockdown.
He is also expected to set a target to ensure the NHS can carry out half a million tests per day by the end of October, to help the NHS Test and Trace programme.
As the health service prepares for what could be the most difficult winter season in its 72 year history, ministers have already announced plans to mount the largest flu vaccine programme the UK has ever seen.
A No 10 spokesperson said the virus was now under control and restrictions have been eased in a “cautious, phased way”.
“But the prime minister is clear that now is not the time for complacency, and we must make sure our NHS is battle ready for winter,” he added.
“He will set out a broad package of measures to protect against both a possible second wave, and to ease winter pressures and keep the public safe.”
Even without the threat of Covid-19, the NHS can struggle in the winter.
A spike in seasonal diseases like flu and norovirus, combined with staff sicknesses, can place the health service under extreme pressure.
In recent years the government has announced extra cash for the NHS to ease those problems, but never on the scale of £3bn before.
Ministers fear the winter will also see the NHS Test and Trace programme under pressure like never before.
Large numbers of cases of flu and other diseases could lead many people to falsely believe they have Covid-19.
The extra funding is for England. Scotland, Wales and Northern Ireland will benefit from Barnett consequentials, where applicable.
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