Henry's father, Thomas Henry, was a manufacturing chemist in Manchester and an analytical chemist of some repute. Initially qualifying as a physician from Edinburgh University, Henry practiced for five years in the Manchester Infirmary. Later he took over the running of the chemical works established by his father.

In 1801 he formulated the law now known as Henry's law, which states that the solubility of a gas in water at a given temperature is proportional to its pressure. His close friend John Dalton was encouraged by this finding, seeing it as a confirmation of his own theory of mixed gases, and the two men discussed the methods of experimentation in detail.