Fajans was born May 27, 1887, in Warsaw, Congress Poland, to a family of Jewish background. After he had completed secondary school in Warsaw (1904), he studied chemistry in Germany, first at the University in Leipzig, and then in Heidelberg and Zürich. In 1909 he was awarded his PhD for research into the stereoselective synthesis of chiral compounds.
In 1910 Fajans took a job at the laboratory of Ernest Rutherford in Manchester, where the nucleus was discovered.  He then returned to Germany, where he became an assistant and subsequently assistant professor at the Technical University of Karlsruhe, researching radioactivity. In 1917 he headed the Faculty of Physical Chemistry at Munich University, and in 1932 became the Head of the Institute of Physical Chemistry established by the Rockefeller Foundation. In 1935 he left Germany due to escalating Nazi persecution. He stayed for a while in Cambridge and then moved to the University of Michigan where he worked until his demise. In 1959 he became an honorary member of the Polish Chemical Society.
Fajans retired at age of seventy but never stopped working. He died May 18, 1975, in Ann Arbor, Michigan.