The increase amounts to £394m a week more than NHS England's current budget, an above-inflation rise that the prime minister said marks the NHS out as the government's 'number one spending priority'.
Speaking at the Royal Free Hospital in Hampstead, Ms May said the government could not continue 'putting a sticking plaster on the NHS budget each year', and that a long-term funding settlement could help it plan with ambition and confidence.
GP leaders have welcomed the rise, but warned it falls short of historic NHS funding increases of around 4% a year. Campaigners and economists have also warned that because the increase applies only to NHS England's budget, the real increase in health spending is closer to 3%.
The Nuffield Trust said that because the funding announcement related to the NHS England budget, it does not cover 'spending on things like training staff, building hospitals and public health' - although the prime minister specifically highlighted better long-term planning around 'technology, buildings and workforce' as factors that the funding boost would help tackle.
Ms May said on Monday: 'It is clear that more money is needed to keep pace with the growing pressures on the NHS. Over the past 70 years, increases in funding have often been inconsistent and short-term, creating uncertainty over what funding will be in as little as two years' time. This has led to a system of planning from one year to the next, preventing investment in technology, buildings and workforce.
'We cannot to continue putting a sticking plaster on the NHS budget each year. So we will do more than simply give the NHS a one-off injection of cash. Under our plan NHS funding will grow on average by 3.4% in real terms each year to 2023/24.
'We wil also provide an extra £1.25bn a year to cover a specific pension pressure. By 2023/24 the NHS England budget will increase by £20.5bn in real terms compared with today. That means it will be £394m a week higher in real terms. So the NHS will be growing significantly faster than the economy as a whole, reflecting that the NHS is this government's number one spending priority.'
The prime minister said that the funding would be 'provided specifically for the NHS', and that part of it would come from a 'Brexit dividend', with the rest to come from increased taxation.
'Across the nation taxpayers will have to contribute a bit more in a fair and balanced way to support the NHS we all use. We will listen to views on how we do this and the chancellor will set out details in due course.'
She criticised previous Labour governments for wasting some additional funding provided for the NHS, warning that the current proposals 'must be a plan that ensures every penny is well spent'.
Speaking on the BBC's Daily Politics earlier on Monday, health minister Lord O'Shaugnessy said in November 'when the chancellor sets out his budget we will have clarity on the different funding mechanisms' that would deliver the increase in NHS funding.
Ms May has also said that budgets for social care and public health will be set out in the government's forthcoming spending review.