The Prime Minister will pledge that the sum, to be paid this year, will also immediately hit frontline services by boosting beds and providing new equipment.
The funding is in addition to Theresa May‘s £33.9 billion yearly increase to go to the health service by 2023/24.
Labour, however, seized on the spending and said it “falls significantly short” of the amount needed to reverse Tory cuts.
The Nuffield Trust health think-tank said the sum will “only be a fraction” of the cost needed to upgrade 20 hospitals as Mr Johnson pledged on his first day as PM.
Mr Johnson’s latest spending pledge is also expected to be used to upgrade wards, repair buildings and boost capital spending.
Some £850 million would go towards funding the vital upgrades to the hospitals.
Labour accused the Tories of “smash and grab raids” by diverting money away from capital spending – used for equipment and repairs – in order to plug funding holes elsewhere in the NHS.
Shadow health secretary Jonathan Ashworth said: “This announcement – even if it’s ever delivered – falls significantly short of what’s needed to provide quality, safe care to patients after years of Tory cuts.
“Tory ministers have repeatedly cut capital investment budgets in recent years. These smash and grab raids have meant over £4 billion slashed and seen the NHS repair bill spiral to £6 billion putting patient safety seriously at risk.”
Nuffield Trust chief executive Nigel Edwards said the money falls far short of what is required.
“This is a welcome down payment on the staggering £6 billion needed to clear the backlog of NHS maintenance but it will only be a fraction of what it would cost to really upgrade 20 hospitals,” he added.
“Nobody should expect shiny new hospitals in their towns any time soon.”
Liberal Democrat health spokeswoman Baroness Jolly said Mr Johnson’s pledge “will not be worth the paper it’s written on” when a no-deal hits.
“The Conservatives have under-funded social care to the point of crisis, they have failed to address a critical staffing shortage while children’s mental health services are almost non-existent,” she added.
Cancer Research UK said the investment would go “some way to address the immense strain” the NHS is under but stressed that funding in recruitment and training is essential to meet rising demand.
Policy director Emma Greenwood added: “Upgrades to hospitals are welcome but the NHS is experiencing a staffing crisis. And it’s impossible to diagnose more cancers at an early stage without the right staff.
“If the new government wants to save more lives, it must give the NHS workforce a cash injection now to make sure there are enough doctors and nurses to diagnose and treat people around the UK for decades to come.”
Delivering on health spending commitments is particularly pertinent to Mr Johnson.
He has faced continual criticism over his referendum battle bus claim that leaving the European Union would allow the UK to take back control of £350 million a week, some of which could be used to boost NHS funding.
The UK Statistics Authority chairman Sir David Norgrove rebuked Mr Johnson and said it was a “clear misuse” of official figures.
Mr Johnson is expected to visit a hospital on Monday to formally announce the new funding and to identify the 20 hospitals to be upgraded.