He was the son of Gérard Savart, an engineer at the military school of Metz. His brother, Nicolas, who was a student at the École Polytechnique and an officer in the engineering corps, did work on vibration. At the military hospital at Metz, Savart studied medicine and later he went on to continue his studies at the University of Strasbourg, where he received his medical degree in 1816. Savart became a professor at Collège de France in 1836 and was the co-originator of the Biot–Savart law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed about 1820. The Biot–Savart law relates magnetic fields to the currents which are their sources.
Savart also studied acoustics. He developed the Savart wheel which produces sound at specific graduated frequencies using rotating disks.