Czibulka was born in Szepesváralja (German: Kirchdrauf, Slovak: Spišské Podhradie), Szepesváralja district of Szepes (Slovak: Spiš), Upper Hungary. He first came to prominence from the age of 15 touring Southern Russia giving piano recitals and concerts. He eventually became musical director at the French Opera in Odessa and at the National Theatre in Innsbruck, in 1865 he was second under Franz von Suppe as conductor at the Carl Theatre in Vienna.
From 1866 to 1869 he served as a military bandmaster in Austro-Hungarian Infantry Regiment No. 17 in Bolzano. From 1869 to 1870 he held the same position at the "23ern" in Petrovaradin and then, until 1871, with Infantry Regiment No. 20 in Krakow.
Success as conductor and composer in the military led Czibulka onwards to Kapellmeister for Infantry Regiment No. 25 in Prague from 1872 to 1880. In 1880 he was appointed representative of Austria-Hungary's military orchestra at the International Exhibition in Brussels. He won First Prize he won 1st prize at that festival's Internationalen Musikkapellenkonkurrenz
As a military bandmaster in the Infantry Regiment No. 31 in Vienna from 1883 to 1887 he held highly acclaimed composer-nights together with the musicians of the "30" under Carl Czerny (not related to the piano teacher). As a civilian he became music director in 1889 of the Concert House Flora in Hamburg. From 1891 to 1894 he again served as a military band conductor at the "19ern" in Vienna.
In the English-speaking world he is today best-remembered for his association with the famous piece Hearts and Flowers which was first a song created from the introduction 2/4 section of his work Wintermärchen Waltzes Op.366 (1891). The soon-forgotten song was re-issued as a stand-alone instrumental under the same title as the song. Hearts and Flowers is the sentimental piece that has been frequently used to indicate mock tragedy in film and cartoon soundtracks.
Czibulka wrote over 300 works, especially Viennese-style dance music and marches. Of his stage works his greatest successes were the operettas Pfingsten in Florenz (1884) and Der Glücksritter (1887). Other oeprettas include : Der Jadjunker, Gil Blas, Der Bajazzo. A substantial amount of his music is preserved in the music collection of the Vienna City Library.
In 1938 a street, Czibulkagasse, was named after him in Vienna's Simmering (11th District).
- Scene de Ballet op. 268
- Erzherzog Friedrich-Marsch op. 286 (1878)
- Stephanie-Gavotte op. 312 (1880)
- Vom Donaustrand, Marsch op. 339 (1887)
- Liebestraum nach dem Balle, Intermezzo op. 356 (1890)<ref>[https://archive.org/details/EdithLorandHerOrchestra.
- Loves Dream After Ball
- An Dich!, Walzer-Serenade op. 390 (1894)
- Friedrich Anzenberger, Alfons Czibulka (1842-1894), Militärkapellmeister und Komponist, Wiener Stadt- und Landesbibliothek 2000, Publikationen der Wiener Stadt- und Landesbibliothek, Band 5.
- "Österreichisches Biographisches Lexikon 1815–1950 (ÖBL). Vol. 1, Austrian Academy of Sciences, Vienna 1957, p. 164. ". In: