He taught at Magdalen College School of Medicine at Oxford and later became the youngest Sterling Professor of Physiology at Yale University.

[1]: S8  After his time at Harvard, he focused his studies on neurosurgery at the Peter Bent Brigham Hospital in Boston under Harvey Cushing.

[2]: 561  He taught briefly at the Magdalen College School of Medicine from 1928 to 1929,[1]: S9  then transferred to Yale University, becoming the youngest Sterling Professor of Physiology.

His positions included editor for the Journal of Neurophysiology;[2]: 561  creator of the Yale Aeromedical Research Unit in 1940;[2]: 561  chairman of the Subcommittee on Historical Records of the National Research Council,[2]: 562  member of the Committee on Aviation Medicine;[2] trustee for the Institute for Advanced Study in Princeton, New Jersey in 1942;[2]: 562  president of the History of Science Society from 1947 to 1950;[1]: S12  first chairman of the Yale Department of History and Medicine in 1951,[3] along with Harvey Williams Cushing and Arnold Klebs,[2]: 560  and head of the Journal of the History of Medicine and Allied Sciences from 1951 to 1960.

[2]: 562 Fulton strongly encouraged the addition of humanities into the scientific fields by placing the history of sciences into general education.

[5] During his time as president of the History of Science Society, he was a member of the editorial board of its historical journal Isis[2]: 560  and helped stabilize it so it could grow in popularity.

He wrote biographies for Harvey Cushing, Benjamin Silliman, Robert Boyle, Girolamo Fracastoro, Richard Lower, John Mayow, Kenelm Digby, and Joseph Priestley.

[7] Fulton's team's findings influenced Portuguese neurologist Egas Moniz, who developed the medical practice of the frontal lobotomy in humans and who won the Nobel Prize for his work in 1949.

It made great progress in the fields of aviation medicine as well as high-altitude flying, which caused Fulton to be awarded various honors (below).