Brueckner completed his Ph.D. in physics at the University of California, Berkeley, in 1950. He was a member of the physics faculty at Indiana University (1951-1955) and the University of Pennsylvania (1956-1959). In 1959, he was recruited by Roger Revelle to come to the University of California, San Diego (UCSD) during its formative years where he became one of the founders of its Department of Physics.

In the mid 1960s, he was a member of the US Atomic Energy Commission Fusion Program Standing Committee, formed by Amasa Bishop to provide advice to fusion program office management. The Standing Committee consisted of the directors of the fusion programs at major US fusion sites plus a few scientists, including Brueckner, from outside the fusion community.

Brueckner was asked by Bishop to form an Ad Hoc Panel of the Standing Committee to review the prospects for using lasers to initiate fusion reactions. The prospects for laser fusion were being studied on a classified basis at AEC weapons laboratories at the time. Brueckner became so enthusiastic about the prospects during the review that he resigned from the Standing Committee, took a leave of absence from UCSD, joined in 1968 the Michigan-based firm of KMS, Inc. headed by Kip Siegel, and began to file patent applications for laser fusion. This resulted in a patent dispute between KMS and the US government that lasted many years. KMS built an impressive laser facility but eventually concluded that laser fusion would require much more time and effort and a much larger laser to succeed. Brueckner left KMS Fusion in 1974 and returned to UCSD. He retired from UCSD in 1991.

He received the Dannie Heinemann Prize for Mathematical Physics from the American Physical Society in 1963 and was elected a Member of the National Academy of Sciences in 1969.