Hellwig was the son of a preacher. In 1789 began learning a trade but received a musical education at the same time from Joseph Augustin Gürrlich, Georg Abraham Schneider and Carl Friedrich Zelter in Berlin. In 1812 he decided to focus solely on Music.
In addition to his position as organist for the court and cathedral in Berlin (1813) and as royal music director (1815) he was also a member of the Sing-Akademie in Berlin, with which he was closely associated for the rest of his life. During an illness of the director, Carl Friedrich Zelter, he also temporarily assumed leadership of the academy and was later named vice director. Hellwig was a founding member of the Zelterschen Leidertafel, which was founded on January 24th, 1809.
He composed many songs, an opera and prepared piano parts for Christoph Willibald Gluck’s “Iphigenie auf Tauris” and Georg Friedrich Händel’s oratorio “Judas Maccabäus” (based on Wolfgang Amadeus Mozart’s piano arrangement).
