Brockhouse was a graduate of the University of British Columbia (B.A., 1947) and the University of Toronto (M.A., 1948; Ph.D., 1950). From 1950 to 1962 he carried out research at Atomic Energy of Canada's Chalk River Nuclear Laboratory. In 1962, he became professor at McMaster University in Canada, where he remained until his retirement in 1984.
He shared the 1994 Nobel Prize in Physics with American Clifford Shull for developing neutron scattering techniques for studying condensed matter.