He originally comes from Lengau in the canton of Aargau and grew up in Zurich as the son of Peter and Hella Müller-Heuer (daughter of Walter Heuer), a central figure in the area of German orthography.
He first studied the cello with Claude Starck at the Zurich Conservatory, but then increasingly dedicated his energies to composition.
He received decisive encouragement from David Zinman, who made a recording with the Philharmonia Orchestra, London, including "Nachtgesänge" with Swedish mezzo-soprano Malena Ernman, the Cello Concerto (1999), played by Müller's wife, the Taiwanese cellist Pi-Chin Chien and two further orchestral works.
Fabian Müller was artistic director of the International Music Festival Lenzburgiade in Switzerland from 2009 to 2013 and he is very interested in ethnomusicology.
Müller's recent works include the opera «Eiger», based on a libretto by the Swiss author Tim Krohn, commissioned by the TOBS Theater Orchestra Biel Solothurn, and a concerto for heckelphone and orchestra for the Swiss oboist Martin Frutiger.