May has announced that NHS England will see an annual 3.4% funding increase in real terms, between 2019 and 2024.
May wrote in the Mail on Sunday that paying smaller contributions to the European Union budget after Brexit would free up money to spend on the NHS, while Downing Street claimed on Twitter that the commitment would be funded by a "Brexit dividend".
In what has delighted Brexiteers, such as Boris Johnson and left Remainers, like Anna Soubry angered, May said that "People may remember seeing a figure on the side of a bus, £350 million pounds extra a week for the NHS in cash".
Independent think tank the International Longevity Centre - UK also welcomed the new funding, but stressed that the growing pressures on the health service need to be managed in the long-term "to avoid this becoming a sticking plaster solution".
When questioned on the Andrew Marr Show on Sunday about what she would be "bringing to the party" ahead of the NHS's 70 birthday on 5 July, Theresa May confirmed the NHS will receive an extra £20bn a year.
"However, if this is to be funded with personal tax freezes and borrowing, then other United Kingdom departments will face funding squeezes to meet the costs of Brexit - and as a result any increases in health could be given with one hand and taken away with the other".
Last month the IFS released a report which considered the impact of increasing NHS funding on other areas of government spending.
The Prime Minister has said that some of the money for the NHS will come from a "Brexit dividend".
Asked about tax increase, May said her finance minister would set out plans before a government spending review expected next year.
"I want to make sure that as see as we see this £2 billion in additional money coming to Scotland that those who work in our health service, who have been telling us that they need this key investment, will see this money coming through".
The move comes as Mrs May faces another turbulent week in Parliament on the Brexit front with Tory rebels again threatening to defy her over how much influence MPs will have over any withdrawal deal.
May also said that one of the priorities of the NHS' ten-year-plan will be "harnessing the power of innovation". (The Treasury is at loggerheads with half the cabinet, as ever.) Leave voters have always been aware of the negative impact of Brexit on the country's finances - after all, they were told enough during the 2016 referendum campaign.
RCGP chair Professor Helen Stokes-Lampard said the "significant amount of money" was "welcome confirmation" that the Government is "committed" to the NHS.
"Well, I can tell you what I am announcing will mean that in 2023-24, there will be about £600m a week in cash, more in cash, going into the NHS".