He is best known for his research in electrocardiography and vectorcardiography, for contributions to understanding viral-based cardiovascular diseases, for 12 books in the field of medicine and cardiology, and for more than 850 publications in the scholarly literature.

A bronze bust of George E. Burch by sculptor Jean Seidenberg is prominent in the main lobby of Tulane University School of Medicine.

[6] His father was a rural general practitioner who involved Burch as a child and teenager in his medical practice, instilling a sense of the excitement and compassion of medicine.

Following medical school graduation, Burch commenced an internship at Charity Hospital of New Orleans, having selected internal medicine for his field of study because of its breadth and depth.

This instructorship gave him formal teaching responsibilities and provided Burch with opportunity to work with practitioners and researchers in the emerging field of cardiology, including John Herr Musser, James A. Bamber, George Herrmann, and Richard Ashman.

[8] Burch's research on the biokinetics of basic metabolites such as water, sodium, potassium, and other ionic species extended to diseases exacerbated in subtropical climates such as are extant in the southern United States.

[9] As an educator, Burch continued clinical teaching at Charity Hospital of New Orleans, with training responsibilities for medical students, residents, and Cardiology Fellows.

[citation needed] Burch became a senior academic with his 1947 appointment to the Chairmanship of the Department of Medicine at Tulane University, holding this position until his retirement in 1975, taking on emeritus status.

[10] He maintained his responsibility as attending physician at the same ward at Charity Hospital, sponsored the Hutchinson Clinic for medical education (created by Charles C. Bass), instituted a tutorial system for medicine residents, and led one of the earliest Fellowship programs for Cardiology Fellows.

[12] Working with the extensive patient population of Charity Hospital, he was instrumental in the discovery of Hemoglobin SS and its relevance to Sickle Cell Disease.

[13][14] Burch was an early pioneer in the use of radioisotopes for diagnostic purposes and for understanding fundamental physiological processes, focusing on electrolyte metabolism in congestive heart failure.

The Matas Library of Tulane University School of Medicine maintains a collection of Burch's artifacts from his father's rural medical practice.