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 10 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 ongoing 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 into these homes over the longer term.
"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."
The council said it has no timescale for the events.
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 that all the options being considered would involve people leaving their homes for at least three months.
At the moment the risk to residents is being managed through the provision of detectors, air quality surveillance and a 24-hour emergency support service which is in place to allow people to be rehomed quickly if necessary.
The council has opened an information office on the estate and housing experts have regularly visited residents.
A special multi-agency project team including an occupational therapist and an NHS public health practitioner is now in place, based at the information office, and will continue to assess the health and housing needs of residents and plan relocations with them under a process known as Care for People.