Wüllner was born in Münster and studied in his native place, and at Frankfurt, Berlin, Brussels, and Munich. Among his teachers was Anton Schindler, who styled himself Beethoven's amanuensis carrying on the true traditions of the master's style, a claim disputed by Beethoven's pupil Carl Czerny. In 1856 Wüllner became instructor in piano at the Munich Conservatory. He held the position of town musical director at Aix-la-Chapelle from 1858 to 1864. In 1867 he became director of the choral classes in the reorganized School of Music at Munich and wrote for them Chorübungen der Münchener Musikschule, text of score reading and singing. He succeeded the temperamental Bülow in 1869 as conductor of the Court Opera and the Academy Courts. Here he conducted the first performances of Rheingold and Walküre before the production of the entire Ring cycle at the first Bayreuth Festival of 1876. It is for these renditions that he is usually remembered now. He became court kapellmeister at Dresden and artistic director of the conservatory in 1877, and director of the Cologne conservatory and conductor of the Gürzenich concerts in 1884. After 1864 he appeared frequently as conductor of the Lower Rhenish Music Festival. He died in Braunfels. Among his notable pupils were Volkmar Andreae, Fritz Brun, Lothar Kempter, Bruno Klein, Jan van Gilse, Hans von Koessler, Karl Aagard Østvig, Ernst von Schuch, and the conductor Willem Mengelberg. Mengelberg controversially claimed that his teacher's ties with Schindler gave Mengelberg a direct connection with Beethoven performance tradition. Among his works are: Heinrich der Finkler, a cantata for solo, male chorus, and orchestra; additional recitatives to Weber's Oberon, accepted by many of Germany's principal theatres; Psalm 125, for chorus and orchestra; Miserere for double choir; and Stabat Mater for double choir; besidesmasses, motets, songs, chamber music, and piano pieces. Wüllner was one of the editors of the Bach-Gesellschaft-Ausgabe, the first complete edition of the works of Johann Sebastian Bach.
Recording
There is a recording fragment in the Thomas Edison National Historical Park archive from 1890 featuring Wüllner at the piano accompanying the singer Karl Mayer in Schubert's 'Wohin?'. This makes Wüllner the earliest-born person whose piano playing has been recorded acoustically. Unfortunately, the recording quality of the Wüllner cylinder is now so degraded that almost nothing can be discerned about the piano playing at all.