He was born in Dijon, France. Despite his father's death in 1817 when he was 14, his mother was able to borrow money to pay for his tutors. In 1821 he enrolled at the École Polytechnique in Paris, and transferred two years later to the École des Ponts et Chaussées (School of Bridges and Roads), which led to employment in the Corps of Bridges and Roads.

Henry met an English woman, Henriette Carey, whose family had been living in Dijon, and married her in 1828.

As a member of the Corps, he built an impressive pressurized water distribution system in Dijon following the failure of attempts to supply adequate fresh water by drilling wells. The system carried water from Rosoir Spring 12.7 km away through a covered aqueduct to reservoirs near the city, which then fed into a network of 28,000 meters of pressurized pipes delivering water to much of the city. The system was fully closed and pressurized by gravity, and thus required no filters or pumps. He was also involved in many other public works in and around Dijon, as well as in the politics of the Dijon city government.

During this period he modified the Prony equation for calculating head loss due to friction, which after further modification by Julius Weisbach would become the well-known Darcy–Weisbach equation still in use today.

In 1848 he became Chief Engineer for the département Côte-d'Or (of which Dijon is the capital). Soon thereafter he left Dijon due to political pressure, but was promoted to Chief Director for Water and Pavements and took up office in Paris. While in that position, he was able to focus more on his hydraulics research, especially on flow and friction losses in pipes. During this period he improved the design of the Pitot tube, into essentially the form used today.

He resigned his post in 1855 due to poor health, but was permitted to continue his research in Dijon. In 1855 and 1856 he conducted column experiments that established what has become known as Darcy's law; initially developed to describe flow through sands, it has since been generalized to a variety of situations and is in widespread use today. The unit of fluid permeability, darcy, is named in honor of his work.

He died of pneumonia while on a trip to Paris in 1858, and is buried in Cimetière de Dijon (formerly known as Péjoces) in Dijon.