Health Secretary Matt Hancock said the planned restructure will mean a focus "on the health of the population, not just the health of patients".
But Labour questioned the timing of the changes "in the middle of the biggest public health crisis our NHS has ever faced", saying staff were exhausted.
Mr Hancock said there was "no better time than now".
A full White Paper was published on Thursday, setting out the proposed future legislation.
"The pandemic has made the changes in this White Paper more not less urgent," Mr Hancock told MPs.
The shake-up will see the law changed to reverse reforms of the NHS in England introduced under Prime Minister David Cameron in 2012.
Ministers believe the changes will put the NHS in a better position to cope with an ageing population and a rise in people with complex health conditions.
One-in-three patients admitted to hospital as an emergency has five or more health conditions, such as diabetes, obesity or asthma, up from one-in-10 a decade ago.
Those working in the health service said many of the rules in place were time-consuming, frustrating and stressful.
Announcing the changes to MPs, Mr Hancock said the new system would see the NHS and local councils take decisions about local health together.
"The new approach is based on the concept of population health," he said.
Organisations called "integrated care systems" - which already exist in some parts of the country - will be set up in each part of England and be responsible for funding to support that area's health.
"They will provide not just for the treatments that are needed but support people to stay healthy in the first place," said Mr Hancock.
Responding to criticism over the timing, Mr Hancock said the pandemic had "brought home the importance of preventing ill health in the first place".
Nigel Edwards, of the Nuffield Trust think tank, said the changes would be a "re-wiring behind the dashboard" and should not be too noticeable to patients.
While it was not a "magic bullet", it could help different parts of the system work more closely together, he added.
Analysis: Why now and what does it mean for patients?
The public will be rightly asking what difference these reforms make and why they are being introduced now in the middle of a pandemic.
The concept predates Covid - councils and the NHS have been piloting these approaches to integrated care over the past few years.
But, in many ways, the pandemic has speeded up the process. With more care being done out of hospital because of the pressures from Covid, community NHS and council care teams have been working ever more closely.
There is much to recommend greater joined up working. The 21st century patient has multiple conditions.
Take a 70-year-old with heart problem and dementia who lives alone. They will need input from a heart specialist, support from community nurses and maybe the company of a befriending service.
The staff needed could come from three different organisations working and funded separately. It creates bureaucracy and it is not hard to see how the quality of care suffers.
The white paper is an attempt to re-wire the NHS. But those working for the NHS argue that is just one part of the solution - staffing and investment will also play a role.
The proposals include scrapping the tendering rule, which sees providers and private companies compete to win contracts to run services.
This rule made it complicated for councils and different parts of the NHS to set up joint teams and pool their budgets, with some having to set up separate bodies to bid for contracts.
Instead, the NHS and councils will be left to run services and told to collaborate with each other to pool resources.
It also gives the health secretary more control over NHS England and other national bodies, which had been given a large degree of autonomy under the 2012 changes.
Social care plan 'this year'
Shadow health secretary Jonathan Ashworth said Labour had long argued for more integrated care, but raised questions over the timing.
He also said the test of the reorganisation "will be whether it brings waiting lists and times down, widens access especially for mental healthcare, drives up cancer survival rates and improves population health".
Mr Ashworth added that "legislation alone of course is not the answer to integration.
"We need a long-term funded workforce plan. We've not got one. We need a sustainable social care plan. We were promised one on the steps of Downing Street. We still don't have one."
The UK's social care system is under pressure with past governments failing to reform or fund the council-run system properly.
In their 2019 election manifesto, the Conservatives pledged to find a cross-party solution to reduce pressures on the sector and provide long-term funding.
Mr Hancock told MPs the government was "committed to the reform of adult social care and will bring forward proposals this year".
Meanwhile, NHS England chief executive Sir Simon Stevens said the reform will create a "flexible can-do spirit" across the health and care system.
The White Paper will cite examples of good practice, such as a care team at the Royal Derby Hospital which sees nurses from the community, council care services and hospital staff working together to plan the discharge of patients.
Chris Hopson, of NHS Providers, which represents NHS managers, said it would end "an unnecessarily rigid NHS approach to procurement".
The Local Government Association welcomed the plans but said they did not provide the funding to put care services on a "sustainable and long-term footing".