Eichberger was born in Würzburg on 23 June 1953. Following his first state exam in law 1979 in Mannheim and his second one in 1981 in Baden-Württemberg he was a research assistant at the University of Mainz until 1984. Afterwards he did his doctoral dissertation there in 1985. Between 1984 and 1986 he was a judge at the administrative court in Karlsruhe. Later, from 1986 until 1989, he worked at the Justice Ministry of Baden-Württemberg. After that he worked at the Federal Constitutional Court of Germany as a research assistant until 1991. Since 1992 he was a judge at administrative court in Karlsruhe again and in 1993 he was delegated as a judge to the Higher Administrative Court of Baden-Württemberg in Mannheim, where he stayed until 1998. Since 1998/99 he was a docent at the University of Tübingen. Between 1998 and 2006 he was a judge at the Federal Administrative Court of Germany in Leipzig as well. 2004 he became an honorary professor at the University of Tübingen. In April 2006 he was appointed as a judge at the Federal Constitutional Court of Germany.