Cartellieri was born in Danzig. His father, Antonio Maria Gaetano Cartellieri, was Italian, and his mother, Elisabeth Böhm, was Latvian. Both of his parents were opera singers and he received his earliest musical education from them. At the age of 13 his parents divorced, at which time Cartellieri moved with his mother to Berlin. In that city he began studying music composition.
In 1791, at the age of 18, Cartellieri became court composer and music director for Count Oborsky in Poland. In 1793, he returned to Berlin with his employer where his first opera premiered successfully. He then went with the Count to Vienna where he continued with further musical studies in music theory and composition under Johann Georg Albrechtsberger and possibly Antonio Salieri.
On 29–30 March 1795, the première of his oratorioGioas re di Giuda took place in Wiener Burgtheater. (In the interval, Beethoven played his piano concerto which became Beethoven’s debut as a composer.) In 1796, Cartellieri was engaged by Prince Joseph Franz Maximilian Lobkowicz (1772-1817) as the Kapellmeister, singing teacher, and violinist, roles he held until his death 11 years later. His other duties at court included directing operas and playing the violin in both concerts of chamber music and symphonic music. He notably performed in the world premières of several works by Beethoven under the composer's baton, including the Eroica Symphony and the Triple Concerto on 23 January 1805. He died in Liebshausen, Bohemia at the age of 34.