The 64-year-old will replace American Cardinal William Levada, who retires from the helm of the Congregation of the Doctrine of the Faith, after seven years as enforcer of Catholic doctrine. It is a position previously held by the pope himself, as Joseph Ratzinger.
Müller, the archbishop of Regensburg in southern Germany, has a reputation as a defender of Catholic orthodoxy and has been criticised by German groups clamouring for change, such as Die Kirche von unten (The Church from Below).
A personal friend of the German-born pope, who charged him with publishing his writings, Müller is however also known for his long-standing support for Gustavo Guttierez, founder of the socialist Liberation theology movement.
His appointment was greeted with apprehension by the grassroots organisation Wir Sind Kirche (We are Church), which said Müller "has been very reserved, hostile" towards fundamentalists in his diocese whose vision of the Church differs.
"A key issue will be to see if his long friendship with the South American liberation theologists will lead to a re-evaluation of that theory, which Ratzinger has fought against down the years," the group said.
His fierce reputation as a conservative, alongside his close friendship with Guttierez reflects a common contradiction in the Vatican hierarchy of openness in some quarters countered by an unshakable hard-line stance on Church morals.
Müller, who travels to Peru almost every year to see Guttierez, defended liberation theology - which champions the poor - in 2008, when he was awarded an honorary doctorate by the Pontifical Catholic University of Peru (PUCP).
But the Vatican has long criticised the movement, seen by some as a fusion between Christianity and Marxism. The Holy See this year also fell out with the university, insisting it come into line with Lima's conservative archbishop.
The Congregation of the Doctrine of the Faith plays a key role in the Vatican's governing body, holding the diverse theological strains within the global Catholic Church to account.
Müller is expected to assume the post in the next few days when Levada retires and will have to take up the reins on a host of unfinished affairs, including the clerical sex abuse scandal which has engulfed the Church.
The watchdog cracks down on dissident factions, from rebellious priests challenging the Vatican's approach to priest celibacy, homosexuality and women in the Church, to feminist nuns in the United States.