[3][4] In 1962, Klitzing passed the Abitur at the Artland-Gymnasium in Quakenbrück, Germany, before studying physics at the Braunschweig University of Technology, where he received his diploma in 1969.

He continued his studies at the University of Würzburg at the chair of Gottfried Landwehr, completing his PhD thesis entitled Galvanomagnetic Properties of Tellurium in Strong Magnetic Fields in 1972, and gaining habilitation in 1978.

During his career Klitzing has worked at the Clarendon Laboratory at the University of Oxford and the Grenoble High Magnetic Field Laboratory in France (now LNCMI), where he continued to work until becoming a professor at the Technical University of Munich in 1980.

[5] The von Klitzing constant, RK = h/e2 = 25812.80745... Ω,[6] is named in honor of Klaus von Klitzing's discovery of the quantum Hall effect, and is listed in the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty.

Klitzing's research focuses on the properties of low-dimensional electronic systems, typically in low temperatures and in high magnetic fields.