Why are the German professors addressed as Prof. Dr. XXX?

In Germany, in rare cases also non-doctors can become a professor. Then it's just "Prof. Müller". Regarding Doctors, we don't have a "PhD" title. "Dr." is the official title for a doctor which is traditionally a prefix to the full name.

See also: http://en.wikipedia.org/wiki/Doctor_(title)#Germany

In Germany, professorships and doctorates are considered to be "legal" titles, and have special status not accorded to other degrees and professions. In particular, university professors in Germany are Beamte (appointed civil servants, sg: "Beamter"/"Beamtin"), which places them in a relatively small class of government employees.

It is to be noted that a professor in a German university can be called "Herr Professor" or "Frau Professorin" only so long as he or she is actively working as a professor. Following retirement or leaving the university profession, it is technically not permitted to use the title.

Thus, in this sense, the appellation "Professor"/"Professorin" is legally part of someone's name, and should therefore be used in formal greetings and salutations. (This can sometimes be annoying—for example, in a physician's waiting room, you can hear them call for "Frau Professorin Schmidt!")