Henry Crew was born in Richmond, Ohio, on 4 June 1859. He attended high school in Wilmington, Ohio, then matriculated to Princeton University in 1878. He graduated in physics in 1882 and was awarded a graduate fellowship at the university for a year, which he spent at the Princeton laboratory. In 1883 he travelled for a semester overseas to study physics in Berlin, returning in 1884 to attend graduate school at the Johns Hopkins University. Three years later he was awarded a Ph.D. in physics.

After a term with an associateship in physics at Johns Hopkins, he became an assistant instructor of physics at Haverford College from 1888–1892. During his last year at Haverford, Henry Crew married to Helen C. Coale, a graduate of Bryn Mawr College. They had one son and two daughters. In 1892 he was awarded the position of Fayerweather professor of physics at Northwestern University, which he accepted. He remained at that post until he retired 41 years later in 1933.

During his career, Crew wrote a number of works on spectroscopy, the history of science, and biographies of physicists, producing 123 articles and 12 books. He was elected president of the American Physical Society in 1909. In 1914 he published, with Albert De Salvio, an English translation of Galileo's Two New Sciences. He served as the president of the History of Science Society in 1930. In 1941 he was awarded the Oersted Medal by the American Association of Physics Teachers. He was named a Chevalier of the Order of the Crown of Italy, and was awarded an honorary degree from University of Michigan in 1914, Princeton in 1922 and Northwestern in 1937.

Crew died on 17 February 1953.