Wüllner was born in Münster and studied in his native place, and at Frankfurt, Berlin, Brussels, and Munich.

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 (Solfege).

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.

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; a setting of Psalm 125, for chorus and orchestra; a setting of Psalm 51 (Miserere) for double choir; and a Stabat Mater for double choir; besides masses, motets, songs, chamber music, and piano pieces.

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?'.