Birkhoff, who was born in Overisel, Michigan, studied at the Lewis Institute (now the Illinois Institute of Technology) from 1896 to 1902, and subsequently at the University of Chicago and at Harvard. In 1907 he obtained his PhD from Chicago and took up a teaching post at the University of Wisconsin, moving to Princeton in 1909. In 1912 he became assistant professor at Harvard and, in 1919, professor there, a post he held until 1939.

Birkhoff's mathematical interests were wide, and among the many areas to which he made notable contributions were differential equations, celestial mechanics, difference equations, and the three-body problem. His main field of research was mathematical analysis, especially applied to dynamics. In the course of his work on dynamical systems Birkhoff obtained a famous proof of a conjecture made by Henri Poincaré in topology, usually known as Poincaré's last geometric theorem. The ergodic theorem, a result concerned with the formal mathematics of probability theory, that Birkhoff proved in 1931, is another of his outstanding achievements. Modern dynamics received an enormous impetus from Birkhoff's work, and he also worked on the foundations of relativity and quantum mechanics.