Bárány has worked at the Kungliga Vetenskapsakademien. He was an editor at Physica Scripta between 1988 and 1996 and secretary for the Nobel committee in physics between 1989 and 2003. Bárány has been the chairman of the Kungliga Vetenskaps Societeten in Uppsala since 1994, and of the Kungliga Vetenskapsakademien since 2005. He was earlier the chairman of the Nobel Museum.