Friedrich Adolf Paneth was born as son of the physiologist Joseph Paneth. He and his three bothers were brought up in Protestant faith although both parents were of Jewish descent. He was educated in the Schotten gymnasium, a renowned school in Vienna. He studied chemistry at the University of Vienna and after working with Adolf von Baeyer at the University of Munich he received his PhD with Zdenko Hans Skraup at the organic chemistry department of the University of Vienna in 1910.

He abandoned organic chemistry and joined the radiochemistry group of Stefan Meyer. In 1913 he visited Frederick Soddy at the University of Glasgow and Ernest Rutherford at the University of Manchester. In this year he married Else Hartmann, they had a son and daughter. After his habilitation in 1913 he became assistant of Otto Hönigschmid at the University of Prague. From 1919 till 1933 he was professor in various German universities. (University of Hamburg 1919, Berlin University 1922, Königsberg University 1929). In 1927 he published his results on the transformation of hydrogen to helium, now known as Cold fusion.

During Hitler's Machtergreifung in 1933 he was on a lecture tour in England and did not return to Germany. In 1939 he became professor at the University of Durham where he stayed until his retirement in 1953.

A call to become director of the Max Planck Institute for Chemistry in Mainz made him return to Germany. He worked in the Institute until his death in 1958.

He was elected a Fellow of the Royal Society in 1947. The mineral Panethite is named after him, as is the lunar crater Paneth.
He was considered the greatest authority of his time on volatile hydrides, and also made important contributions to the study of the stratosphere.