The funding will also help ease winter pressures on the health service, Downing Street said.
It follows warnings a second wave this winter could see around 120,000 Covid-19 deaths in UK hospitals.
The PM is also expected to use a press conference on Friday to commit to a new target for testing capacity.
Under the plans, capacity would be increased to 500,000 coronavirus tests a day by the end of October.
Mr Johnson will also publish an additional chapter to the government's Covid-19 recovery strategy "road map".
Downing Street said the funding would be available immediately and would allow the NHS to continue using additional private hospital capacity and maintain the temporary Nightingale hospitals until the end of March.
This would provide additional capacity for coronavirus patients, as well as allowing the NHS to carry out routine treatments and procedures, No 10 said.
Non-urgent operations were suspended to free up hospital beds as the UK went into lockdown during the first wave of coronavirus - but in May NHS England told hospitals they should restart.
n normal times an announcement of £3bn to help the NHS in England cope with winter pressures might look generous.
But these are not normal times as the government pumps tens of billions into the economy to soften the blows of the coronavirus crisis.
The head of NHS England, Sir Simon Stevens, has been in talks with the Treasury to get guarantees that the Nightingale hospitals can stay open through until next spring in case there is another Covid surge.
He also wanted secure funding in place to do a deal with private hospitals to help tackle the backlog of cancelled non urgent operations such as hip and knee replacements.
That money now seems to have been secured, though we await further details.
The question is, will this be enough to get the health service through what could be one of the most difficult winters in its history?
There have been predictions that the waiting list for routine surgery will swell to 10 million as fears of a second wave of Covid cases in the depths of winter won't go away.
A No 10 spokesman said: "Thanks to the hard work and sacrifices of the British people, the virus is under control and we have eased restrictions 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.
"Tomorrow, 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."
The spokesman said the funding for England was new and not previously allocated, while expenditure will be set out for the devolved nations in due course.
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