Henry Edmund Meleney received his education at Dartmouth college (B.A. 1909) and Columbia University College of Physicians and Surgeons (M.D. 1915). Afterhis internship, Meleney served as a captain in the United States Medical Corps (1917-1918) and a resident pathologist at Presbyterian Hospital, New York. He then accepted a position at Peking Union Medical College in China, where he remained from 1920-1927 researching a number of parasitic disease problems.

Meleney returned to the United States in 1927 and accepted a position in the Department of Preventive Medicine at Vanderbilt University School of Medicine. Here, with the assistance of Dr. W.W. Frye, Meleney studied the problem of amebiasis from the epidemiological, clinical, and experimental standpoints, producing a series of papers. He also served as associate epidemiologist for the Tennessee Department of Public Health.

In 1941 Meleny became the Biggs Professor of Preventive Medicine at New York University College of Medicine, a position he held until 1953. He focused on increasing tropical medicine and parasitic disease education and served as Chair of the Subcommittee on Tropical Diseases of the National Research Council (1940-1946). He retired from New York and accepted a position as Research Professor of Medicine at Louisiana State University before retiring as Professor of Medicine Emeritus at the University of Florida College of Medicine in 1963.