He was appointed Corresponding Member of the Siberian branch of the Soviet Academy of Sciences on March 28, 1958, and was made an Academician of the division of nuclear physics on June 26, 1964.

He is best known for his invention in 1968 of electron cooling, a method of reducing the emittance of particle beams by thermalisation with a co-propagating electron beam.

Academician Budker was the founder (in 1959) and first Director of the Institute of Nuclear Physics in Akademgorodok, Russia. His portrait decorates the famous Round Table room in the Institute. Following his death, the institute was renamed the Budker Institute for Nuclear Physics in his honour.

Budker died in Akademgorodok from a heart attack at 59.

Budker's life and works was celebrated in a collection of essays by his colleagues, including Pyotr Kapitsa, Lev Landau, and Andrei Sakharov, and two by Budker himself. The collection, G.I. Budker: Reflections & Remembrances (edited by Boris N. Breizman) was published in 1988 and was later translated into English by James W. Van Dam.