The spending plan was announced during the summer when £20bn was promised to the service. About 23,000 premature deaths could be prevented by putting 100,000 people with heart complaints through a healthy living and exercise programme every year.
Matt Hancock, the Health Secretary, said: "The NHS long term plan, backed by a historic commitment of an extra £20.5billion a year from taxpayers, marks an important moment not just for the health service but for the lives of millions of patients and hardworking NHS staff across the country".
The NHS says the measures, which will also see adults with rare conditions receive genomic analysis, will ensure early detection of three out of every four cancers by 2028, up from the current rate of one in two.
Mrs May said that the ambitions set out in the plan, which several experts warned would be hard to achieve, was affordable in part because the United Kingdom would no longer be sending "vast annual sums" to Brussels after it leaves the European Union.
NHS England chief Simon Stevens said the plan also "tackles head on" the pressures faced by health staff.
The plan forecasts that primary care and outpatient services will change over the next 10 years to a model of tiered escalation depending on need, in which senior clinicians will be supported by digital tools.
Efforts to tackle respiratory conditions and prevent 80,000 hospital admissions will see patients given "smart inhalers" which are Bluetooth-enabled so patients' conditions can be monitored wherever they are. It will also provide for genetic testing for a quarter of people with dangerously high inherited cholesterol, reaching around 30,000 people.
The plans will also see Global Positioning System and community services get a larger share of the funding, with £4.5billion a year put aside, and mental health services expanded to help 345,000 more children and young people.
- Cutting-edge scans and the potential use of artificial intelligence to improve stroke care.
A Department for Health spokesman added: "By 2024 we want every patient in England to be able to access a GP services digitally, with practices able to offer online or video consultations".
Investment in mental health services will rise to at least £2.3 billion a year by 2023/24 - a move which has been praised by mental health charity Mind.
"Too often, those with gambling addiction suffer in silence, which is why we will continue to work closely with the NHS to help make sure there are good links between the services we commission and those commissioned by the NHS".
Royal National Institute for Blind People's eye health policy manager, Helen Lee, said the focus on prevention and the use of technology within the long-term plan was welcome.
The plan was welcomed by campaigners, but experts warned that implementing it would be hard.
"It sets a practical, costed, phased route map for the NHS's priorities for care quality and outcomes improvement for the decade ahead".
Plans unveiled today to deliver a NHS plan fit for the future with a focus on more integrated community care, saving more lives and promoting the use of digital technology has been welcomed by Staffordshire County Council's health chief. "And while commitments for the NHS to do more to promote public health are welcome, cuts to local government funding for public health services underline the need for a more consistent approach across government to the population's health".
Other significant elements of the plan include: improving out-of-hospital care by supporting primary medical and community health services; also drawing on these to support older people through more personalised care; and an emphasis on improving maternity safety. But the plan cannot escape the harsh reality that the NHS will still face tough decisions on what it can and cannot do.