Tenants from 110 St Michael's Street in Shrewsbury were evacuated last Friday after a resident raised the alarm with Shropshire Council.
A structural engineer has been inspecting the house, and temporary traffic lights have been in place this week to keep the public well back.
The engineer's assessment found that the building is a danger to the public, so the owner has confirmed the building can be demolished.
The property, which is not listed and had a number of rented rooms, has been evacuated and the residents have been put into emergency accommodation.
The council is working with the owner to find a demolition contractor to carry out this work as quickly as possible to minimise disruption and neighbouring owners are being informed.
A section of St Michael’s Street between the Flaxmill roundabout and New Park Road will be closed to through traffic until the demolition is complete. Traffic will be diverted via New Park Road and Sultan Road.
There will still be access for anyone needing to get to their home or business along St Michael’s Street for the period of the closure.
Councillor Ed Potter, Shropshire Council’s cabinet member for economic growth, regeneration and planning, said: “The council has taken immediate action because we have a building on a main road in imminent danger of collapsing. Considering the danger to the public, safety must come first and we have agreed to allow the building’s demolition and hope that this can happen as quickly as possible.
“We appreciate this will lead to some disruption for residents and businesses in the area and trust they will understand the urgent nature of this.
“We hope that any disruption can be kept to as short a period as possible and we will keep residents updated via our website and social media.”