Miliband made the pledge in a speech that had a strong focus on higher wages, creating jobs and increasing the number of apprenticeships available.
He vowed to increase funding for the NHS with higher taxes on the tobacco industry, a 'mansion tax' on wealthy homeowners and more government borrowing if necessary.
Through these means he claimed there would be up to £2.5 billion of extra funding for the NHS, enough to pay for 20,000 more nurses, 8,000 extra GPs, another 5,000 care workers and 3,000 midwives.
Miliband claimed the larger workforce would help to revive the "creaking" NHS.
"One-in-four people wait a week or more for a GP appointment," he said. "We have seen the scandal of care visits restricted to just 15 minutes for the elderly. It is time to care about the NHS so that doctors, nurses, care workers and midwives are able to spend proper time with us, and not [be] rushed off their feet.”
Unite general secretary Len McCluskey welcomed Miliband's comments, claiming "the NHS will be safe under Labour".
"Ed Miliband demonstrated his commitment to the NHS with the pledge of 36,000 more doctors, midwives and nurses," he said.
Miliband also outlined six goals for Britain, with a strong focus on employment. These goals included halving the number of low paid workers, backed up by the recent pledge to increase the minimum wage to £8 per hour, and increasing the number of apprenticeships.
City & Guilds UK managing director Kirstie Donnelly welcomed the call for more apprenticeships but warned the focus must be on quality as well as quantity.
"What we need now are details from Labour about how these additional apprenticeships will be created and how they intend to ensure that quality remains high," she said. "We know from experience that simply promising more apprenticeships is not enough.
"We need schools to offer robust careers advice so young people are aware of their options, and we also need to see businesses work with awarding bodies to ensure consistent high-quality training."