The prime minister said this will be partly funded by a "Brexit dividend" - money Britain will supposedly save from no longer contributing to the European Union's budget.
However speaking to the Today programme this morning, Hunt admitted the Brexit dividend "alone won't be anything like enough".
It is expected tax and borrowing will rise to pay for the increase in funding.
The NHS has been struggling to cope with funding shortages in recent years, particularly during the flu-ridden winter months.
A £20bn boost - £394m a week - promises to go further than the infamous Brexit bus slogan, which vowed to offer the NHS the £350m a week now being "sent" to the EU.
Eight years of austerity has lumbered the NHS with record waiting lists, the worst-ever performance in A&E last winter and a profound staffing crisis.
She attacked the Cameron government's key health reform - driven through by the former Health Secretary, Lord Lansley - which created clinical commissioning groups to negotiate legal contracts with other parts of the NHS.
Germany follow trend of poor starts for World Cup champions
That defeat to Germany followed a 7-0 mauling at the hands of Chile a year earlier at the Copa America Centenario. Also in Group F, Sweden topped South Korea in their match today and Belgium is now on the pitch with Panama .
"As we celebrate the fact that our NHS is 70 years young, it's important we look to how we deliver the sustainable health and social care communities across Scotland will require in the future", she added.
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". "It must be a plan that enjoys the support of NHS staff across the country - not something dreamt up in Whitehall and centrally imposed".
"So we have to see the detail and see where this money is going to come from we have to see that it is going to be real money". We will listen to views about how we do this and the Chancellor will set out the detail in due course.
The announcement of more cash for the country's healthcare system, a regular issue at national elections, comes after a row in parliament over Brexit highlighted the fragility of May's minority government.
The Prime Minister has said that some of the money for the NHS will come from a "Brexit dividend".
"The debate over Brexit can be divisive, but that famous campaign promise can now unite us all: the British public voted for £350 million a week for the NHS, and that - and more - is exactly what this government will deliver", Hunt said.
Spending billions of pounds is cool again.
"I'm one of those people that have relied on the NHS throughout their entire life".