After a classical education at West Nottingham Academy in Colora, Maryland,[3] he graduated from the College of Philadelphia, now the University of Pennsylvania, in 1757.

[1]: 18 [4] He fought for the British during the Seven Years' War, and was commissioned as a lieutenant and served as a surgeon on the western frontier.

He subsequently toured Western Europe, studying medical practice in Paris and visiting Italy.

Morgan served as chief physician to the Continental Army from October 1775 to January 1777 during the American Revolutionary War and was empowered by the Continental Congress to inspect regimental hospitals and transfer patients if warranted and to examine regimental surgeons.

Rancour among the regimental surgeons became so extensive that Morgan quit following the Continental Army's move from Boston to New York City.