The homes in Gorebridge, Midlothian, were built from 2007 to 2009 without special protective barriers,known as gas membranes, underneath.
Problems came to light in September last year when two people sought hospital treatment and five homes were vacated after special air-quality monitoring equipment found higher than normal levels of carbon dioxide.
A special meeting of the council yesterday agreed to the demolition of 54 homes on Newbyres Crescent and ten on Gore Avenue.
The final decision on what should happen to the cleared land will be delayed until the multi-agency group managing the public health implications of the situation has completed its analysis of an options appraisal.
Owen Thompson, leader of Midlothian Council, said: "I can only imagine the worry and distress being experienced by residents in these homes and demolition is the only option which will rule out entirely the possibility of further leaks of carbon dioxide.
"Our planning can now accelerate and we will ensure we work with each individual resident, together with our NHS colleagues, to support them as much as possible in the process of finding them alternative permanent tenancies meeting their needs."
He added: "Our first priority is protecting residents' health. Meanwhile we are currently taking legal advice in relation as to whether any of the consultants or contractors engaged by the council failed to comply with their legal obligations."
It is investigating the possibility of bringing forward plans to build new homes in the Greenhall area of the town as part of its plan to find alternative permanent properties for residents.
The residents were told in May all the options being considered would involve people leaving their homes for at least three months.
The risk to residents is being managed through the provision of detectors, air quality surveillance and a 24-hour emergency support service.