Brockhouse was elected a Fellow of the Royal Society (FRS) in 1965. In 1982, Brockhouse was made an Officer of the Order of Canada and was promoted to Companion in 1995.
Brockhouse shared the 1994 Nobel Prize in Physics with American Clifford Shull of MIT for developing neutron scattering techniques for studying condensed matter.
In October 2005, as part of the 75th anniversary of McMaster University's establishment in Hamilton, Ontario, a street on the University campus (University Avenue) was renamed to Brockhouse Way in honour of Brockhouse. The town of Deep River, Ontario, has also named a street in his honour.
The Nobel Prize that Bertram Brockhouse won (shared with Clifford Shull) in 1994 was awarded after the longest-ever waiting time (counting from the time when the award-winning research had been carried out).
In 1999 the Division of Condensed Matter and Materials Physics (DCMMP) and the Canadian Association of Physicists (CAP) created a medal in honour of Brockhouse.  The medal is called the Brockhouse Medal and is awarded to recognize and encourage outstanding experimental or theoretical contributions to condensed matter and materials physics. This medal is awarded annually on the basis of outstanding experimental or theoretical contributions to condensed matter physics. An eligible candidate must have performed their research primarily with a Canadian Institution.