Deaconess House dates back to 1894 when it opened as a hospital until its closure in 1990.
More recently, the building was used as office accommodation.
The original Deaconess House is being retained and refurbished and demolition work has already taken place to clear the site of the redundant outbuildings.
Graham has just started work on the 65-week construction programme.
Three new blocks will be created to the rear of Deaconess House and will be situated around a central courtyard, which will include an amphitheatre and hard and soft landscaped areas.
The new blocks will rise to four or five storeys and will contain a total of 315 bedrooms, split across a mix of studio apartments and 3, 5 and 6 bedroom units.
Mace Real Estate has already signed an agreement with Edinburgh University, which will take over the new student accommodation complex once construction work is completed.
Contracts manager at Graham Construction Paul McBurney said: “We have significant experience of student accommodation projects for colleges and universities around the UK, including at Stirling, Newcastle and for the University of the West of Scotland in Paisley.
“While Deaconess House isn’t listed, we are treating it as a listed building and will be taking every care to ensure this property is returned to its former glory.
“This will be an interesting construction challenge as we seek to integrate the old with the new and create something which will compliment the surrounding buildings in this historic quarter of Edinburgh.”
Graham will use a combination of materials, including natural stone and powder coated aluminium panels on the new build elements of the project. An extensive part green roof will also be created.