Dessauer was born into a wealthy Jewish family, and studied piano in Prague with Bedřich Diviš Weber and composition with Wenzel Tomaschek. Dessauer began as a song composer, but later began composing operas, of which very few were performed.
In 1821 he settled in Vienna, from which he made many European tours. He was a friend of many composers of his time, such as Gioachino Rossini, Franz Schubert, Hector Berlioz, Felix Mendelssohn, Franz Liszt and Frédéric Chopin, who dedicated some pieces to him.
- Lidwinna (1836)
- Ein Besuch in Saint-Cyr (1838)
- Paquita (1851)
- Domingo (1860)
- Oberon (which was never performed)
- "Das Gebet"
- "Wie Glücklich"
- "Am Strande"
- "Ich Denke Dein"
- "Das Zerbrochene Ringlein"