As a theologian, teaching in Erlangen and Göttingen, he focused on the history of the Reformation, and was editor of the Theologische Realenzyklopädie.

He received international recognition such as a membership of the Royal Netherlands Academy of Arts and Sciences and an honorary doctorate from the University of St Andrews.

[4] On 1 October 1982, he became Landesbischof of the Lutheran Church in Brunswick, with its seat in Wolfenbüttel, serving until 31 May 1994.

[3] Faced with rising numbers of people leaving the church, he supported projects seeking more intense contact with members such as the missionary "Neu anfangen".

[3] Müller was elected a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1979.