Eichhorn was born in Munich and studied in music in Würzburg. From 1945, he directed the Munich Philharmonic Orchestra, conducted the Bavarian People's Opera and Dresden Philharmonic Orchestra, and taught conducting at the Munich Academy of Music. He was appointed honorary conductor of the Bruckner Orchestra in Linz and in 1991 the Bruckner Association of Upper Austria awarded him the Gold Plaque.
Eichorn died in Murnau in 1994.