Paul, who was born at Lorenzkirch in Germany, was educated at the universities of Kiel and Berlin, where he obtained his PhD in 1939. After World War II, he taught physics at Göttingen until 1952, when he was appointed professor of physics at the University of Bonn.

During the 1950s he developed the so-called Paul trap as a means of confining and studying electrons. The device consists of three electrodes – two end caps and an encircling ring. The ring is connected to an oscillating potential. The direction of the electric field alternates; for half the time the electron is pushed from the caps to the ring and for the other half it is pulled from the ring and pushed towards the caps.

For his work in this field Paul shared the 1989 Nobel Prize for physics with Hans Dehmelt and Norman Ramsey.