He became a student of Svante Arrhenius at the Nobel Institute at a young age and was on the way to Jean-Baptiste Perrin in France when World War I broke out and he was drafted into the military.

In 1923, he received a professorship at University of Michigan in Ann Arbor and moved there with his recently wedded wife, Gerda Koch from Denmark.

Klein returned to Copenhagen in 1925, spent some time with Paul Ehrenfest in Leiden, then became docent at Lund University in 1926 and in 1930 accepted the offer of the professorial chair in physics at the Stockholm University College, which had previously been held by Erik Ivar Fredholm until his death in 1927.

Walter Gordon,[4] independently discovered and published the equation a few months later, as well as Vladimir Fock.

[7][2] The Oskar Klein Memorial Lecture, held annually at the University of Stockholm, has been named after him.