The son of the Lucka town musician Christian Gottlieb Pölcke, Belcke first played the French horn before switching to the trombone at the age of twelve to fill a vacant position in the town orchestra. In 1811 he became a pupil of the town musician Sachse in Altenburg and later his successor when he had to go to war. In 1815, he appeared in the ''Leipzig Gewandhaus'' as solo trombonist with a Concertino for bass trombone and orchestra by Carl Heinrich Meyer and was thus probably the first trombone soloist to be heard in a German concert hall.
His appearance made such an impression that the Gewandhaus Orchestra engaged him as bass trombonist. He undertook concert tours to Merseburg, Halle and Dessau and was engaged in 1816 as royal chamber musician in Berlin. At the invitation of Carl Maria von Weber, he performed at a court concert in Dresden in 1817 but declined to join the Dresden Court Orchestra. In the following years his reputation as a trombone virtuoso grew, he undertook concert tours through Denmark, Sweden, Holland, France and Austria and received the ''Gold Medal of the Paris Conservatory'' in 1844.
On leaving the Royal Chapel in Berlin in 1858, Belcke was awarded the ''Order of the Red Eagle'' r. In the following years he went on concert tours with his brother, the flutist Christian Gottlieb Belcke. He also performed a number of compositions for trombone, including concertos and several etudes.
