Henry was the son of Thomas Henry. He studied medicine and chemistry at Edinburgh, and later took his MD in 1807 with a dissertation on uric acid. However he spent much of his career engaged in chemical work; in 1803 he communicated to the Royal Society his work on the absorption of gases by water, and stated Henry's law. in 1808, he was made a Fellow of the Royal Society. He also undertook research on coal gas. Henry was a member of the Manchester Literary and Philosophical Society.
Henry was a physician at MRI from 1808-1817. Although he was always more interested in chemistry, he undertook researches into combating contagious diseases. He died in 1836 and was buried at Cross Street Chapel, Manchester.