Incumbent agency Finsbury, which held the account for over five years, was invited to re-pitch for the business, a spokeswoman for Assura said.
Edelman has been hired to promote Assura across a range of stakeholder groups including financial and investor, central and local government, as well as potential customers. Work began this month.
Assura, which designs, manages and builds GP surgeries and NHS primary care centres, has a property portfolio valued in excess of £1.3bn.
Mav Wynn, director at financial comms and investor relations consultancy, Smithfield, which Edelman acquired in 2015, will lead the account, focusing on investor relations and account coordination. The public affairs side will be run by Lucy Thomas, who played a leading role at Stronger In before becoming an associate director in Edelman's 20-strong government relations and public affairs team.
Wynn said: "Assura has a truly unique story to tell, a strong investment case and plays a fundamental role in the future of Britain's most revered institution, the NHS. We firmly believe that our fully integrated approach to communications, which includes capital markets, corporate communications and public affairs, makes us perfectly placed to support the company's ambitions."
Edelman is the world's largest PR agency, recording global revenues in 2016 of more than $874m (£664m), according to the PRWeek Agency Business Report 2017.