Welser-Möst, 54, whose glittering career has included conducting the world-famous Vienna New Year's Concert last year, cited "long-held conceptual differences in artistic matters" for his decision.
The Austrian's immediate departure leaves the opera house's French head Dominique Meyer without a conductor for a string of planned performances in the 2014-2015 season including two opera premieres.
Welser-Möst trained as a violinist before a car accident turned him to conducting, working with orchestras around the world including in London, Berlin, Zurich, Philadelphia and New York.
Last year he pulled out of conducting a three-year cycle of Mozart operas at the Salzburg Festival, saying that a start-time of one performance at 11:00 am meant the singers would have to wake up at 3:00 am "to be ready".
According to specialist music blog Slipped Disc, Möst had significant musical differences with the head, Meyer. "There are differences over the artistic direction which did not occur overnight. Dominique Meyer, as director, is the number one. He is a very decent human being with different opinions on artistic matters. That is his standpoint. But then I must accept the consequences", he said.
He went on to say "It is to do with singers and conductors, to do with the whole area that involves the artistic direction of the house… Believe me: This is a very painful decision for me. Especially after this singularly happy Rosenkavalier at Salzburg, it wont be easy for me to give up working with this orchestra [the Vienna Philharmonic - ed.]".
Meyer responded with his own statement, saying "I greatly admire Franz Welser-Möst as an artist and conductor. My concern and my first task is to find as quickly as possible an adequate replacement for the performances he should be conducting at the Vienna State Opera in the 2014/2015 season: at least 34 performances, including two premieres, Rigoletto and Elektra."
According to music expert Norman Lebrecht of Slipped Disc, "There had been, we hear, a dispute over a forthcoming production of Josephslegende, a Richard Strauss ballet, a work for which the conductor has strong feelings. The choreographer and ballet company felt differently. Tensions simmered."
"But this was not the reason for the sudden breach. A meeting was held yesterday in which the music director expressed his views for the company’s medium-term future. They diverged markedly from those of the administration. It was decided that both sides would go home and sleep on the matter.
First thing this morning, Franz came in and submitted his resignation to Meyer with immediate effect. Like Mahler, like Karajan, like Abbado, he will not set foot in the Vienna Opera again. An era is over. Too soon."