Kotani was born in Kyoto and spent his primary and middle school days in Osaka.

In 1929, he received his BSc degree in physics and was appointed as a lecturer at the faculty of engineering in the Imperial University of Tokyo.

In 1965, he moved to Osaka University as a professor in the faculty of engineering science.

This was for his joint work with Sin-Itiro Tomonaga on the theory of magnetrons and microwave circuits.

He received the 1969 Tohyoh Rayon Prize for the work in quantum mechanical study of molecular electronic structure, the 1974 Fujiwara Award for his contribution to the basic studies of molecular physics and biophysics, and the 1977 International Society of Quantum Biology Award.