Fort House, in Leith, will be bulldozed within weeks but work could last all summer, owing in part to the fact that some sections of the property are now listed.
DSM has won the contract for the demolition.
After building is completed on the site, it will house 100 new homes designed by Malcolm Fraser Architects in the colony style.
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Ricky Henderson of Edinburgh Council said the development, on a site which had become notorious for drug taking and criminal activity, illustrated the challenge of "trying not to make the mistakes of the past".
He said: "Having Malcolm Fraser involved gives me every faith that there will be something appropriate and sympathetic."
Colonies were used from the late 19th century in Edinburgh as model dwellings for skilled working-class families.
They were designed as two-floor houses with each floor serving as a flat.
As part of the current redevelopment plans, three flat owners and 151 tenants were re-housed from the Fort House block in November 2009.
Archaeologists working on the site discovered remains of an 18th-century military fort last October.
The perimeter wall, entrance gate and guardhouse are now all listed.
But parts of the wall may be removed to allow sunlight in for residents of the planned housing.
(NE/GK)
