The concept of a "Brexit dividend" has been widely criticised, with health and social care select committee chair and former GP Sarah Wollaston calling it "tosh".
It is expected that taxes and borrowing will rise to pay for the increase in funding, and resources will be redirected from the more than £9bn a year the United Kingdom now pays into the EU.
The NHS has been struggling to cope with funding shortages in recent years, particularly during the flu-ridden winter months.
Plus, the funding increase announced focuses only on NHS England.
The funding is supposed to come in part from a much debated "Brexit dividend", which the government argued would bring £9 billion into the struggling health services.
The settlement would equate to an average increase of around 3.4 per cent per year over the next five years.
Echoing this, the Office for Budget Responsibility (OBR) recently projected that NHS spending would have to increase by 5.3% of national income over the next 50 years if it is to meet increasing demand for its services and other cost pressures.
Health secretary Jeremy Hunt this morning agreed that Brexit could raise some of the money but conceded "more resourcing" through other means was necessary.
He warned: "There is no Brexit dividend".
"We will listen to views about how we do this and the chancellor [Philip Hammond] will set out the detail in due to course".
"With this extra spending power, Northern Ireland now has the opportunity to improve health outcomes for our people and create the NHS that they deserve".
Meanwhile, in a sign of arguments likely to be made by Tory MPs, John Penrose, a senior backbencher, has said that Hammond should commit himself and future chancellors to only borrowing money for "long-term investments" in infrastructure, rather than day-to-day spending on areas such as the health service.
Asked about the scepticism over the Brexit dividend - official forecasts are that departing the European Union will cost the public purse around £15bn a year, while much of the European Union contribution has already been allocated for the next few years - May insisted it existed.
"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".
"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. As a country, we need to contribute a bit more in a fair and balanced way".