The anchor store will be part of a much bigger plan to redevelop the 20-acre former hospital site, which was left vacant when services moved to the new Royal Derby Hospital in May 2009.
The hospital trust submitted plans for the Nightingale Quarter development at the end of last year.
As well as a 50,000 sq ft supermarket with more than 350 car parking spaces, the plans include building 300,000 sq ft of offices, a hotel and around 450 homes.
Work to prepare the former hospital site for the arrival of Morrisons has already begun, with a £4m redevelopment project due to be completed by October.
Construction work should get underway after that to open the store next year.
Derby hospitals’ director of finance and information, Lee Outhwaite, said there had been keen interest from all the leading supermarket operators.
He said: “The choice of Morrisons was a strategic one. Unlike other supermarket operators, it is chiefly a grocery business and concentrates on selling food and doesn’t have significant other lines, such as clothing or electronics.”
Money from the sale of the site – the amount of which is not yet being revealed by health chiefs – will be reinvested in health care projects.
The council also announced a few months ago that it would invest £28m in the new quarter building a 50-metre swimming pool with teaching and toddlers’ pools.