And praising Mrs May, she said: "The Prime Minister today could not have been clearer, that the NHS is her number one spending priority, that's why there is this cash injection".
In a speech in London, the prime minister will stress the NHS must ensure "every penny is well spent".
Echoing this, the Office for Budget Responsibility (OBR) recently projected that NHS spending would have to increase by 5.3% of national income over the next 50 years if it is to meet increasing demand for its services and other cost pressures.
Any increase in funding for the health service in England is reflected in the Barnett formula, used to distribute Treasury funds across the devolved nations.
This year's NHS budget is £114bn. The International Longevity Centre calculated that if things carry on as they are, health spending could rise from around 6 percent of GDP in 2019-20 to 16.4 percent by 2064-65, which would be completely unsustainable. Instead, Mr Grieve accused pro-Brexit hardliners in his own party of seeming to "prefer chaos", rather than reach an agreement to give MPs a voice in the process.
"That's not just me that's saying that, but we've had the health committee chair Dr Sarah Wollaston calling it tosh and criticising the UK Government for treating the public like fools and of course we've had the Institute for Fiscal Studies saying there's no Brexit dividend". "By the end of the meeting, some sources of funding had been more heavily pencilled in than others", a ministerial source said.
The PM has set aside an additional £1.25 billion each year on top of the settlement to cover specific pensions pressure in order to focus the extra investment on frontline care, a Downing Street spokesman said.
To increase taxes would be to break a manifesto pledge, while funding cuts elsewhere would further frustrate a public and cabinet who have grown exhausted of austerity.
"It must be a plan that tackles waste, reduces bureaucracy and eliminates unacceptable variation", she will say. "It must be a plan that enjoys the support of NHS staff across the country - not something dreamt up in Whitehall and centrally imposed". And even after that it would still need 4% more than it's now getting.
"As we celebrate the fact that our NHS is 70 years young, it's important we look to how we deliver the sustainable health and social care communities across Scotland will require in the future", she added.
"But that alone won't be anything like enough, so there will also be more resourcing through the taxation system, and also through economic growth".
"I believe the best days for our NHS are ahead of it - this financial commitment by the Conservatives will let our health care professionals work to build a stronger, safer and better NHS for all of us".
Johnson, who was visiting Geneva to address the U.N. Human Rights Council, dismissed the idea that many people thought relying on a "Brexit dividend" was nonsense.
- Extra cash will be made available to Scotland, Wales and Northern Ireland under the Barnett formula.