Composer and singer of Moravian-Bohemian descent; little is known about his youth. In 1740 he became Vice-Kapellmeister to Prince-Abbot Anselm von Reichlin-Meldegg in Kempten, Allgäu. By 1747 Richter was a court musician of the Elector Palatine Carl Theodor in Mannheim, and he probably performed as a singer at the Mannheim court opera. He wrote a composition treatise, Harmonische Belehrungen oder gründliche Anweisung zu der musikalischen Ton-Kunst oder regulären Komposition (MS, ed. and trans. C. Kalkbrenner as Traité d'harmonie et de composition, Paris, 1804), and embarked on a number of concert tours, first at the Oettingen-Wallerstein court (1754), and subsequently in France, the Netherlands, and England. Around 1768 the elector appointed him chamber composer; in 1769 he succeeded Joseph Gamier as Kapellmeister at Strasbourg Cathedral.
Burney considered Richter one of the best of the Mannheim composers; his contrapuntal writing, though somewhat conservative, was particularly admired, and his symphonies (approximately 80 are extant), string quartets, and sacred music (including thirty-nine Masses) are generally well crafted. His pupils included J. M. Kraus, Ferdinand Fränzl, and Karl Stamitz.