The firm has just struck a deal with fast-growing German budget hotel group Motel One to anchor the mixed scheme, which also includes offices, flats and two restaurants.
It is understood that contractor Crisp Building and Renovation will carry out much of the building work at the Market Street site, which was once home to the council.
Chris Stewart said: “Bringing Motel One in to anchor the whole development kick starts the regeneration of a key part of the Old Town.
“Motel One were introduced to me by Scottish Development International at the annual International Investment Hotel Forum in Berlin and it was clear that they were actively looking at the UK.
“Edinburgh was high on their target list and although this site has been challenging for us due to its sensitive nature and historic context, we were sure it could provide Motel One with everything they were looking for.
“I hope that Market Street is the first of many projects which we do with Motel One.”