He was born in Strasbourg to a Protestant family of Alsatian descent.
After studying law and music, he moved to Paris in 1774 where he played and taught the piano.
In late May 1794 he was arrested after a false accusation of treason (he was in fact an opposer of the terroristic policy and paid the hatred of Saint-Just).
Sentenced to death by the Revolutionary Tribunal on 17 July 1794 (29th Messidor), he was executed the same day by guillotine in Place de la Barrière du Trône together with his brother Louis, other two Strasbourg citizens, and the sixteen Carmelite nuns of Compiègne (only eleven days before the fall of Robespierre).
Edelmann composed two operas, an oratorio and various pieces of chamber music.