Harry Washington Greene was born in New Bern, North Carolina on February 28, 1896, the son of Elvin and Sophia Greene. His parents had been denied access to education and were illiterate. Greene was able to surpass the educational opportunities of his parents, going on to receive numerous degrees and ultimately become a college administrator himself. He graduated as valedictorian of his high school in 1911 and attended Lincoln University in Pennsylvania from 1913 to 1918, where he received both his bachelor's and master's degrees. From 1919 to 1920 Greene attended the Yale Divinity School, where he was secretary of the Alpha Phi Alpha Fraternity. He subsequently received a master’s in education from Columbia University in 1927. While his career as a college administrator drew more on his background in education, he was an active member of the African Methodist Episcopal Church.
Greene married Leola Stanley in 1920, and in 1922 he began his career as a college administrator, taking a position as Dean of Samuel Huston College in Austin, Texas. Throughout his career he worked at two other historically Black colleges, acting as dean of Prairie View State College (1928-1930), also in Texas, and as director of the School of Education at West Virginia State College (1930-1952). Greene held a number of other significant positions in education, becoming the first Black man to head the Central Texas Teachers' Institute in 1925 and acting as a long-time member of the National Society for the Study of Education and the National Advisory Committee on Negro Education, among other institutions. He also wrote several books on the subject of education and Black educational achievements, including The PhD and the Negro (1928), Criteria of Teacher Excellence (1933), An Adventure in Experimental Cooperative Teaching (1938), Financing Higher Education in West Virginia (1945), and Holders of Doctorates Among American Negroes (1946).
Greene died on February 18, 1952 in West Virginia after a rapid illness.