Geiger was born at Neustadt in Germany and studied physics at the universities of Munich and Erlangen, obtaining his doctorate (1906) for work on electrical discharges in gases. He then took up a position in England at the University of Manchester, where he worked with Ernest Rutherford from 1907 to 1912. In 1912 he returned to Germany, from then until his death holding a series of important university positions, including director of the German physical laboratory, the Physikalisch Technische Reichsanstalt, in Berlin (1912), and professor of physics at Kiel University (1925).

Geiger, a pioneer in nuclear physics, developed a variety of instruments and techniques used for detecting and counting individual charged particles. In 1908 Rutherford and Geiger, investigating the charge and nature of alpha particles, devised an instrument to detect and count these particles. The instrument consisted of a tube containing gas with a wire at high voltage along the axis. A particle passing through the gas caused ionization, and initiated a brief discharge in the gas, and the resulting pulse of current could be detected on a meter. This was the prototype, which Geiger subsequently improved and made more sensitive; in 1928 he produced, with W. Müller, a design of counter that is now widely used (and known as the Geiger–Muller counter). With their primitive counter Rutherford and Geiger established that alpha particles are doubly charged helium atoms.

Other important work of Geiger was his investigation with E. Marsden in 1909, of the scattering of alpha particles by gold leaf; this led Rutherford to propose a nuclear theory for the atom.