Harding was born in Lauenburg. From 1786-89, he was educated at the University of Göttingen, where he studied theology, mathematics, and physics. In 1796 Johann Hieronymus Schröter hired Harding as a tutor for his son. Schröter was an enthusiastic astronomer, and Harding was soon appointed observer and inspector in his observatory.
In 1804, Harding discovered Juno at Schröter's observatory. He then went to Göttingen to assist Carl Friedrich Gauss. There he was professor of astronomy.
In addition to Juno, he discovered three comets, and published:
Atlas novus coelestis (1808–1823; re-edited by Jahn, 1856) which catalogued 120,000 stars
Kleine astronomische Ephemeriden (edited with Wiessen, 1830–35)
the fifteenth in the series of Sternkarten of the Berlin Academy's publications (1830)