• A one-off boost of $282.5m over three years to clear the Covid-19 care backlog
• Ongoing funding of $31.350m per annum ($125.4m over four years) to reflect demographic changes and increasing prices.
The Government's best estimate is there's about 153,000 more surgeries and procedures, radiology scans and specialist appointments that need to be done to catch up from the Covid-19 disruption, the ministers said.
And Clarke said this would likely take years, need creative solutions and help from the private sector.
But he hoped the catch-up would be quicker than the amount of time the money was allocated for.
The $282.5m one-off boost is on top of an additional $31.35m a year to reflect a growing and ageing population, increasing costs and previously agreed wage increases.
The massive $3.92b boost for health boards would tackle "the legacy of debt" from a decade of under-funding for the health system, Clark said.
"For too long we've been asking them [for] more and more without giving them all of the resources that they need."
In October, DHBs were revealed to be $1b in the red.
National Party health spokesman Michael Woodhouse welcomed the much-needed funding for health boards but said the injection wouldn't even cover that $1 billion deficit.
Woodhouse said the financial performance of health boards had "nosedived" under the Government and Covid-19 had created significantly more pressure.
"Our DHBs have been left between a rock and a hard place by a Minister who has let them sink into enormous deficits over the past two years."
Today, Clark said it was no secret a number of health boards were running significant deficits and it would take years to get them back in the black.
The spending announcement also came with a warning to health boards to ensure they improved their financial stability.
New Zealanders would expect "every dollar" to be spent in their interests, Clark said.
"I want to be very clear. I do expect DHBs to work on improving their financial performance.
"I will be holding our DHBs to account on this. As the Government has already shown, we are willing to step in where we don't see that improvement happening."
The funding would be distributed based on population and demographics and would be detailed in the Budget.
Clark said a lot of the strain from Covid-19 had come from the health system being under strain.
The extra $980m per year takes the annual budget for DHBs to $15.274b. DHBs are also contracted by the Ministry of Health on behalf of the Crown to provide additional national services.
"Part of the strain has been the neglect of the health system for some time. It has been under-funded, it has been stretched and strained, so we've been determined as a Government to put more money in," Clark said.
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The Health Minister was expecting to receive Heather Simpson's Health and Disability System Review in the coming weeks.
But now was not the time to restructure the health system, Robertson said.
"For us, getting into a drawn-out debate about the structure of our health system would actually let New Zealanders down. They need their services now and we're funding them at record levels."
Asked whether New Zealand could afford this extra funding, Robertson said: "We can't afford not to.
"We have to have strong public services and I think if there's one thing Covid-19 has shown us, it's that having a strong, well-funded health system is critical to the wellbeing of New Zealanders."
Robertson said a big focus of Budget 2020, dubbed "Rebuilding Together", would be ensuring public services like education and health were properly funded.
As a result, some of the other planned initiatives had been put on ice in light of Covid-19, he said.
"There are some things though, that you do not put on ice - they are more important than ever."
Robertson said the Budget was "one staging post" in the recovery to Covid-19.