Hartmut Müller initially received his first musical training on the trumpet as a student of his father. He later switched to the tuba and then studied in Wuppertal and Aachen, where he also completed his concert exam as a student of Walter Hilgers. Already during his studies, he worked in many top-class German symphony and opera orchestras. He then initially belonged to the RSO Saarbrücken before accepting a permanent position with the Wuppertal Symphony Orchestra in 1988, where he is the principal tuba player.
Alongside his work as an orchestra musician, he soon discovered the possibilities for solo and chamber music performances on the tuba. As a soloist and as a founding member of the Melton Tuba Quartett, he quickly made a name for himself beyond the borders of Germany. His concerts have taken him to the USA, Japan, Italy, France, Spain and Portugal, among other places.