That's a faster increase than in recent years, .
The Scottish and Welsh governments will receive an extra £2bn and £1.2bn respectively, with hundreds of millions more allocated for health spending in Northern Ireland.
What do the experts think?
RCGP chair Professor Helen Stokes-Lampard said the "significant amount of money" was "welcome confirmation" that the Government is "committed" to the NHS.
Scottish Health Secretary Shona Robison said extra funding was welcome.
The health service in Northern Ireland is set to benefit from around £600m extra funding a year in real terms by 2023.
While the 3.4% boost has been widely welcomed, the IFS has stated that an increase of at least 4% is needed if services are to improve.
"That money will be coming back".
He said: "Nobody believes she's going to find this money from a so-called Brexit dividend". There isn't any extra guaranteed money available as a result of ending our payments to the European Union budget, because those savings are likely to be more than offset by other costs associated with Brexit.
"When we have that plan in November, we will say "This is a great plan, we accept that it is going to lead to improvements in cancer care and mental health and so on".
After the worst winter on record for the NHS, the much-loved institution is in dire need of fresh funds but a decade of severe spending restraint means the extra cash will nearly certainly have to be generated by increasing taxes, something the Conservatives have traditionally been reluctant to do, though opposition to the idea appears to be softening.More news: Britain condemns Israel bias at United Nations rights council
More news: Elon Musk sends company email about 'extensive and damaging sabotage' by employee
More news: Japan tops Colombia 2-1 in latest World Cup surprise
That could include reducing spending elsewhere. We do know - the Treasury has done its sums, it hasn't made its final decisions but it is very clear this can be affordable.
May also said taxpayers will have to contribute more to pay for the increased health spending. The specifics of how this will work haven't yet been outlined. It has been estimated that the measure could raise nearly £4 billion by the end of this Parliament.
Cancelling a proposed fall in Corporation Tax-from 19% to 17% in 2020-could raise around £6 billion. Without tax increases, Hammond would nearly certainly be forced to abandon his plans to erase the budget deficit by the middle of the next decade.
It also explores what would happen if a dedicated NHS tax was introduced, more information on that is available here.
He said the financial settlement with the EU, plus the UK's commitments to replace EU funding, "already uses up all of our EU contributions" for the next few years. However, that's still less than the 3.7 percent average rise the NHS has had since 1948.
Plus, the funding increase announced focuses only on NHS England.
But she added: 'It is essential that as more details of her long-term plan are announced, general practice is recognised for the vital role it plays in delivering safe, effective patient care in the community, and keeping the entire NHS sustainable'.
The announcement, which comes as the NHS is due to turn 70 years old next year, will be funded in part via a "Brexit divident", Ms May claimed.
"We also remain concerned about the fate of social care".
"People are waiting longer and in pain because of Tory cuts to the NHS", he said.