Jordan was educated at the Institute of Technology in his native city of Hannover and at the University of Göttingen, where he obtained his doctorate in 1924. He left Göttingen in 1929 for the University of Rostock and after being appointed professor of physics there in 1935, later held chairs of theoretical physics at Berlin from 1944 to 1952 and at Hamburg from 1951 until his retirement in 1970.

Jordan was one of the founders of the modern quantum theory. In 1925 he collaborated with Max Born and in 1926 with Werner Heisenberg in the formulation of quantum mechanics. He also did early work on quantum electrodynamics. He developed a new theory of gravitation at the same time as Carl Brans and Robert Dicke.