Mrs May is setting out the five-year budget to mark the 70th anniversary of the health service and says the extra money will come from what is being termed a “Brexit dividend”.
She will announce that money that no longer needs to be sent to the EU after Britain leaves the bloc will help fund the increase.
Taxpayers will also be asked to contribute more for the NHS and the government will be forced to borrow money.
The announcement means the NHS will receive an extra £384m a week – a further £34m than promised in the controversial pledge advertised on the side of the Leave campaign bus in the run up to the referendum.
A long-term plan will be drawn up with help from doctors to set out how the resources should be allocated.
“As the prime minister announces a historic long-term funding boost and 10-year plan for the health service, we are backing the NHS to show the world what a cutting-edge 21st century healthcare system can look like too,” said Health Secretary Jeremy Hunt.
“This long-term plan and historic funding boost is a fitting birthday present for our most loved institution.
“Like no other organisation could ever hope to be, the NHS is there for every family at the best and worst of times, from the wonder of birth to the devastation of death, living and breathing those very British values of decency, fairness and compassion.”
Mr Hunt added that the money will create an opportunity for the NHS “to write an entirely new chapter in its history”.
Writing in The Sunday Telegraph, Mr Hunt said: “The debate over Brexit can be divisive, but that famous campaign promise can now unite us all: the British public voted for £350m a week for the NHS, and that – and more – is exactly what this Government will deliver.”
Sustainable long-term funding for the NHS could cost £2,000 for every household in Britain, or the equivalent of 9p on income tax, two respected think tanks previously told Sky News.
Simon Stevens, chief executive of NHS England, said: “As the NHS turns 70, we can now face the next five years with renewed certainty.
“This multi-year settlement provides the funding we need to shape a long-term plan for key improvements in cancer, mental health and other critical services.”