One of the first great American scientists, Henry came from a poor background in Albany, New York, and had to work his way through college. He was educated at the Albany Academy, New York, where he first studied medicine, changing to engineering in 1825. A year later he was appointed a professor of mathematics and physics at Albany. In 1832 he became professor of natural philosophy at Princeton (then the College of New Jersey) where he taught physics, chemistry, mathematics, and geological sciences, and later astronomy and architecture.

Henry is noted for his work on electricity. In 1829 he developed a greatly improved form of the electromagnet by insulating the wire that was to be wrapped around the iron core, thus allowing many more coils, closer together, and greatly increasing the magnet's power. Through this work he discovered, in 1830, the principle of electromagnetic induction. Soon after, and quite independently, Michael Faraday made the same observation and published first. Faraday is thus credited with the discovery but Henry has the unit of inductance (the henry) named for him. However, Henry did publish in 1832 – prior to Faraday and Heinrich Lenz – his discovery of self-induction (in which the magnetic field from a changing electric current induces an electromotive force opposing the current). Earlier (in 1829) he had invented and constructed the first practical electric motor. In 1835 he developed the electric relay in order to overcome the problem of resistance that built up in long wires. This device had an immediate social impact for it was the key step in the invention of the long-distance telegraph, which played a large part in the opening up of the North American continent. In 1846, he became the first secretary of the Smithsonian Institution, which he formed into an extremely efficient body for liaison between scientists and government support of their research. He also did work on solar radiation and on sunspots.