The NHS in England is to get an extra £20bn a year by 2023 as a 70th "birthday present", Theresa May says.
It means the £114bn budget will rise by an average of 3.4% annually - but that is still less than the 3.7% average rise the NHS has had since 1948.
The prime minister said this would be funded partly by a "Brexit dividend", but also hinted at tax rises.
Labour said the government had failed to fund the NHS properly and was relying on a "hypothetical" windfall.
Shadow health secretary Jonathan Ashworth said Labour's taxation plans meant his party could match the Conservatives' spending plans and "will go further".
In her BBC interview, Mrs May did not spell out how the £20bn a year would be funded but said: "As a country we will be contributing more, a bit more, but also we will have that sum of money that is available from the European Union."
But Commons Health and Social Care Committee chairwoman Sarah Wollaston described the idea of a Brexit dividend as "tosh".
The Conservative MP accused the government of using "populist arguments rather than evidence".
And the director of economic think tank the Institute for Fiscal Studies (IFS), Paul Johnson, has tweeted to say "there is no Brexit dividend".
The five-year funding settlement covers just front-line budgets overseen by NHS England.
About a 10th of the overall health budget is held by other bodies for things such as training and healthy lifestyle programmes, including stop smoking services and obesity prevention programmes.
The BBC understands these will be protected, but beyond that it is unclear what will happen to them.
The 2015 spending review - the last time a five-year settlement was announced - saw these budgets cut to help pay for an £8bn increase in NHS England's budget.
Year-by-year funding increases
- 2019-20 - 3.6%
- 2020 - 21 - 3.6%
- 2021-22 - 3.1%
- 2022-23 - 3.1%
- 2023-24 - 3.4%
All figures are above inflation
The announcement means extra money will also be made available for Scotland, Wales and Northern Ireland, although it will be up to the Welsh and Scottish governments to decide how that is spent.
'Don't forget social care'
Speaking to the BBC's Andrew Marr, Mrs May acknowledged that pressure had been growing on the NHS, which was founded 70 years ago, and said her formal announcement on Monday would be about "securing its future".
"We're going to ensure there's a 10-year plan for the NHS," she said. "That will be a plan for world-class health care - more doctors, more nurses. It means extra money - significantly more money going into the NHS."
Mr Ashworth told the BBC's Sunday Politics that Labour's tax plans meant it would be able to spend more but added the exact percentage of how much it could increase spending by would have to wait until the chancellor presented his own spending plans.
And shadow chancellor John McDonnell dismissed the government announcement as a "publicity stunt", adding: "Can you imagine if I came forward with this? There'd be accusations of magic money trees. This is a magic money forest that's come out this morning."
Chris Hopson, chief executive of NHS Providers, which represents NHS trusts, said the government's settlement was the "minimum" that was needed.
"After almost a decade of austerity, the NHS has a lot of catching up to do."
By Jonathan Blake, BBC political correspondent
Step back from the big figures and the arguments about Brexit and there is something significant in Theresa May's announcement.
A Conservative prime minister promising more money for public services, with the implication that taxes could go up to pay for it.
Because when Mrs May talks about "contributing more as a country" that is what she means.
You'll struggle to find a politician arguing against a boost for the NHS, but there might just be one or two Tories privately questioning whether this portrays them as a tax-and-spend party.
Support for the NHS is such a big political prize that Mrs May appears willing to go against traditional Conservative low-tax instincts.
The government clearly feels the detail on funding is for another day.
There will be difficult decisions ahead - but the prime minister appears to be saying "trust me".
Mr Hopson also pointed out that the government needed to work out what it was going to do about social care run by councils.
Ministers have promised the system, covering care homes and help at home, will be reformed soon to ensure there is better access to services.
And Niall Dickson, chief executive of the NHS Confederation, which represents healthcare organisations, said the announcement "isn't a bonanza by any means" and that it fell short of the of the 4% extra-a-year figure an independent report had suggested was needed.
However, he added: "It's a lot better than we've been used to over the last few years."
And Ian Dalton, head of regulator NHS Improvement, said the settlement was good news for the NHS and would "enable the dedicated staff in our NHS to go on improving the care we can offer the patients".
Is a 'Brexit dividend' paying for this?
In her BBC interview, Mrs May said the funding boost was partly coming from a "Brexit dividend".
"Some people may remember seeing a figure on the side of a bus a while back of £350m a week in cash," she said.
"I can tell you that what I'm announcing will mean that in 2023-24 there will be about £600m a week, more in cash, going into the NHS.
"That will be through the Brexit dividend. The fact that we're no longer sending vast amounts of money every year to the EU once we leave the EU."
But she also conceded that "as a country" we will need to contribute more.
She did not spell out that would require tax rises, although a recent report by the IFS said they would be needed because it was hard to imagine the money could be found from economic growth or raiding other areas of government spending.
And Mr Johnson said the government had accepted Brexit would weaken the public finances and the financial settlement with the EU plus commitments to replace EU funding "already uses up all of our EU contributions" for the next few years.
Analysis: What difference will this make?
There has been a lot of speculation that Health Secretary Jeremy Hunt - supported by NHS England chief executive Simon Stevens - had been pushing for close to 4% a year extra.
This was the figure many in the health service had said was needed to get services back on track and to improve waiting times.
Reports have suggested the Treasury were initially offering less than 3%.
So the 3.4% average appears to be a compromise between the two camps - and is close to the 3.7% average increase the NHS has seen if you look back over the past 70 years.
So what will this mean? The final picture is somewhat clouded by the lack of clarity about what will happen to the wider health budget.
However, talk to those working for the health service and they say this was the "bare minimum" that was needed to keep services going. They say tough choices will still be needed and that the public should not expect a dramatic increase in performance - targets for cancer, A&E and hospital operations are all being missed.