The review was launched amid a spate of ageism claims against health services. Researchers found elderly stroke patients received less adequate care than younger counterparts and a watchdog warned the over-65s lost out on mental health services.
A poll found almost half of doctors who cared for older people believed the NHS was "institutionally ageist". Officials made clear that the new rights would still be subject to clinical decisions on questions such as prioritising which patients should get vaccines first. Restrictions would also apply in areas such as fertility treatment.
Mr Burnham, who will address the National Children and Adult Services Conference, said: "As we live longer and as the NHS helps us live longer, we have to look at different ways the NHS can help older people."
Equality Minister Harriet Harman said: "It's not acceptable to discriminate against someone because they are older. People are not over the hill at 60 - they shouldn't be discriminated against in health care or in any other way.
"With the number of people over 85 set to double in the next 20 years, it is essential that older people are not written off because of their age. The Equality Bill will end age discrimination and ensure older people can play a full role in society and that they are treated fairly."