The development contains a collection of listed structures and buildings which were originally an agricultural market established in the early 20th Century.
Developer Watkin Jones said these have deteriorated over the years and now “require significant investment”.
It also said: “Through discussion with the council and Historic Environment Scotland, the development retains and refurbishes the most important elements around a publicly accessible heritage square.”
The development will have air source heat pumps and photovoltaic panels.
Iain Smith, planning director at Watkin Jones, said: “Securing approval from Scottish ministers for this landmark regeneration project in Chesser is another step in addressing the city’s housing shortage.
“Following the Scottish government’s declaration of a national housing emergency in 2024, our new development helps to address Edinburgh’s housing needs across several tenures by delivering high-quality homes in a highly accessible location.”