From September 2017, up to 1,000 NHS staff will be able to take up the training without having to go down the conventional university route to get a nursing degree.
Health Secretary Jeremy Hunt says it complements the nursing associate role announced a year ago.
Both initiatives aim to offer flexible routes into nursing in England.
They might also give students an affordable way to train, since ministers plan to scrap student bursaries for nurses in September 2017.
Student nurses at university are currently entitled to bursaries of £4,500 to £5,500 if they live in London - on top of a grant of £1,000 each year during their course.
The course fees are also covered.
But the government has proposed scrapping these and introducing university fees to bring health staff in line with other students.
The NHS will still provide some financial support towards expenses such as travel costs for placements.
Trainees on the apprenticeship scheme will typically be funded by the trust they work for and can join the course at different stages, depending on their qualifications and experience, and stay in work while learning.
Similarly, nursing associates get their training paid for while remaining in work.
At the end of the training - which will usually take five years - a nurse apprentice will have a nursing degree, whereas a qualified nursing associate would still need more training to become a registered nurse.
The Royal College of Nursing said it was great news that there would be more training places and opportunities for staff, but it would be important to ensure any new courses fulfilled educational needs.
Its chief executive, Janet Davies, said: "Nursing has progressed over many years, we must be careful to learn from the lessons of the past when student nurses were often seen as nursing on the cheap.
"We must be careful we do not create a two-tier system which reduces equality of opportunity.
"We need to attract people of all ages and from diverse backgrounds into the profession."
Mr Hunt said: "Nurses are the lifeblood of our NHS, but the routes to a nursing degree currently shut out some of the most caring, compassionate staff in our country.
"Not everyone wants to take time off to study full time at university, so by creating hundreds of new apprentice nurses, we can help healthcare assistants and others reach their potential as a fully trained nurse."
Chief nursing officer Prof Jane Cummings said: "The nursing degree apprenticeship offers a new, exciting route into nursing that is open to more people whether they are working within the NHS already or would like to pursue a career in nursing."