He takes over from Michael Finn, who served for 10 years.
The appointment was made by communities minister Andrew Stunell. BRAC is the consultative body that provides strategic and technical guidance to the government on standards for the design, sustainability and construction of buildings.
Mr Cooper, a chartered surveyor, joined BRAC in 2006 and has been deputy chair of the committee since February 2009. Before joining MLM in 2008 he was head of the building control surveying group at the National House Building Council.
Peter Caplehorn, Alan Crane and Stephen Wielebski have also been re-appointed to serve a further three-year term as members of the committee.
Mr Stunell said: "I would like to thank Michael Finn for his outstanding contribution in his 20 years as both member and chair of the Building Regulations Advisory Committee. Under Michael's leadership the committee has been instrumental in helping to deliver safe, healthy, accessible and sustainable buildings across the country.
"But I am sure that under Neil Cooper's chairmanship, the committee will continue to play a key role, particularly given the increasing focus on sustainability and energy efficiency of buildings. I very much look forward to working with him.
"I would also like to thank Peter Caplehorn, Alan Crane and Stephen Wielebski who have all agreed to serve a further term as members of the committee. They bring experience and expertise in their respective fields and have been re-appointed to ensure the high quality of advice provided by the committee is maintained."
Mr Cooper said: "I am delighted and privileged to be appointed to the position. The committee has made a positive and vital contribution to effective regulation under Michael's leadership and I intend to ensure this continues. We face many challenges in respect of delivering sustainable buildings, as well as ensuring appropriate and achievable standards are in place to provide healthy and safe environments. I look forward to working with my colleagues to help the Minister achieve this."