Born in Germantown, Philadelphia, Harrison graduated from Johns Hopkins University in 1889 and continued studying experimental embryology for the next ten years at Bryn Mawr College, Johns Hopkins University, and in Germany at the University of Bonn. He had an excellent ear for languages and spoke German fluently. In 1899 he gained his MD degree from the University of Bonn and returned to America to become associate professor of anatomy at Johns Hopkins. From 1907 to 1938 he worked at Yale, first as professor of anatomy and then from 1927 as professor of biology.

Harrison's work in experimental embryology formed a bridge between the morphological studies of the 19th century and the new molecular biology of the 20th century based on cell function and structure. In his most influential work (1910) he demonstrated the outgrowth of nerve fibers from ganglion cells in embryonic tissues by devising techniques so that the event could actually be observed. His early attempts used frog-embryo cells hanging in a nutrient medium from the underside of a special microscope slide. The method was gradually refined to give the important new technique of tissue culture. Although Harrison himself did not pursue tissue culture to any great extent the method has proved immensely useful in testing new drugs and in the production of vaccines.

Harrison founded the influential Journal of Experimental Zoology in 1906.