Ohm, who was born at Erlangen in Germany, seems to have acquired his interest in science from his father, a skilled mechanic. He studied at the University of Erlangen and then taught at the Cologne Polytechnic in 1817. From 1826 to 1833 he taught at the Military Academy in Berlin, moving to the Polytechnic at Nuremburg before finally obtaining a chair in physics at Munich in 1849.

Despite the fact that he published his famous law in 1827 in his Die galvanische Kette mathematisch bearbeitet (The Galvanic Circuit Investigated Mathematically) he received no recognition or promotion for more than twenty years. Ohm seems to have been stimulated by the work on heat of Joseph Fourier. The flow of heat between two points depends on the temperature difference and the conductivity of the medium between them. So too, argued Ohm, with electricity. If this line of thought is pursued it soon leads to the general form of Ohm's law that the current is proportional to the voltage. Using wires of different sizes he was able to show that the resistance was proportional to the cross-sectional area of the wire and inversely proportional to its length.

Ohm also worked on sound, suggesting in 1843 that the ear analyzes complex sounds into a combination of pure tones. This result was rediscovered by Hermann von Helmholtz in 1860.

The unit of electrical resistance, the ohm, was named in his honor.