The property, located at 97 Bath Street, Sedgley, was formerly a shop which was run by a family known well in the local area.
The building was listed as a historical site but fell out of use for many years and became a target for fly-tipping and anti-social-behaviour.
It had been suggested on social media that the building could be transferred to the Black Country Living Museum, but a spokesman for the attraction denied this.
Demolition is now underway after Dudley Council granted planning permission on February 9 for developers to flatten the site, and build the new three-bedroom properties.
A planning report said: "The site has been disused for many years and the site has been subject to extensive fly-tipping and anti-social behaviour.
"Police and fire services have been called to site on several occasions, with fires and further damage caused to the building.
"Despite efforts to secure the site, unauthorised access to the site has continued.
"The property is a detached, double-fronted 19th century dwelling house.
"The indicative development is for five residential dwellings with private amenity space to the rear and driveways with ample parking for three cars.
"The site will have a uniform layout with a staggered building line."
Planners said they had considered retaining the building but a survey of the property revealed it was unsafe to enter.
The former owners were given planning permission to convert the building into a greengrocery and general store on January 10, 1958.
An earlier application to covert the house into a coal shop and business on September 30, 1955, was refused.
In recent months, a metal fence surrounded the perimeter as they building had fallen out of use.
When the new homes will be built, each property will be equipped with two double bedrooms, an en-suite, a family bathroom and study.
The loft space will be used to create a master bedroom with en-suite too.