Derby Hospitals NHS Foundation Trust wanted to develop the site of the Derbyshire Royal Infirmary on London Road.
But the city council had objected to the demolition of the main Edwardian building.
Following a planning inquiry in February, the government has decided the sale should be permitted.
The scheme, known as the Nightingale Quarter, will include a Morrisons store and about 400 houses and is expected to create about 300 jobs.
But it provoked strong opposition from the city council.
Philip Hickson, Conservative leader at the time the authority considered the plans, said: "The hospital just want the cash and don't give a fig what the city centre looks like. All they're interested in is getting the money."
In a report, the Communities Secretary Eric Pickles
 said there was "no persuasive evidence that the ... proposal would be likely to undermine the vitality and viability of the city centre".
He said of the hospital: "Its significance is limited due to the unexceptional quality of the building as originally constructed."
Lee Outhwaite, director of finance at Derby Hospitals NHS Foundation Trust, said the decision was "very good news for Derby".
He added: "We are now able to continue with our plans for the sale of the site, which will generate a significant amount of funds to be invested in healthcare for the people of Derby and Derbyshire.
"We look forward to working more closely with the city council, particularly on the elements of the redevelopment proposal which will benefit ourselves and the council, such as the 'health hub' part of the scheme."
The city council said it would comment once it had studied the report in detail.
A plan to replace a former Derby hospital with a supermarket and houses has been approved.