Müller studied chemistry at the University of Stuttgart from 1959 to 1963. He worked on his dissertation at the Purdue University and the University of Stuttgart. He finished it in 1966 in the group of Kurt Dehnicke. From 1967 to 1970, he worked in the group of Hartmut Bärnighausen at the University of Marburg. In 1972, he finished his habilitation. From 1972 to 1975, Müller was a professor for inorganic chemistry at the University of Marburg. From 1975 to 1977, he was a guest professor at the University of Costa Rica. Then, several professorships for inorganic chemistry followed: University of Marburg from 1977 to 1992, University of Kassel from 1992 to 1999, and University of Marburg from 2000 to 2005. Since 2005, he has been an emeritus professor.