Heller had been destined for a legal career, but instead decided to devote his life to music. At the age of nine he performed Dussek's concerto for two pianos with his teacher, F. Brauer, at the Budapest theater. He played so well that he was sent to study in Vienna, Austria, under Carl Czerny. Unable to afford Czerny's expensive fees, he became a student of Anton Halm. After a success in the first public concert in Vienna at the age of 15, his father undertook a concert tour through Hungary, Poland and Germany.
Heller returned to Budapest by way of Kassel, Frankfurt, Nuremberg, Hamburg, and Augsburg. After passing the winter of 1829 at Hamburg, he was taken ill at Augsburg in the summer of 1830. He abandoned the tour there and was soon afterwards adopted by a wealthy patron of music.
At the age of 25, he travelled to Paris, where he became closely acquainted with Hector Berlioz, Frédéric Chopin, Franz Liszt and other renowned composers of his era. Here Heller eventually achieved distinction both as a concert performer and as a teacher. In 1849 he performed in England, where in 1850 he was the subject of a long serial (that is, divided between many issues) article devoted to his music in the British Musical World, and in 1862 he played Mozart's E-flat concerto for two pianos with Charles Hallé at The Crystal Palace. With these brief interruptions, the last twenty-five years of his life were spent at Paris. He outlived his reputation, and was almost forgotten when he died in 1888. He taught piano to Isidor Philipp who later became the head of the piano department of the Conservatoire de Paris.