He was able to attend the Thomasschule zu Leipzig and was a pupil of Johann Adam Hiller there, but became an orphan at an early age and studied law at the request of his grandfather.
His pupils included among others Henriette Grabau-Bünau, the daughter of the Bremen organist Lebrecht Grabau, with whom Riem also worked.
At the beginning of his term of office he had the work of the organ rebuilt and enriched with romantic voices to achieve a stronger fundamental tone.
In 1815, he founded the Bremer Singakademie with other music lovers, and was generally also its conductor (cathedral cantor) until his death.
For his tomb, the sculptor Diedrich Samuel Kropp [de] designed a free-standing large sandstone figure as a "muse of mourning" in the shape of Saint Cecilia.