The Cori Family came from the Papal State (later Republical Rome, today's Central Italy) to the Royal Bohemian Crownland, Austrian Circle (Monarchical Austria centered on the Archducal Austria) at the end of the 17th century. Carl Ferdinand's grandfather Eduard Cori (1812–1889) was an administrative officer and beekeeper in Brüx, and grandmother was Rosina Trinks (?–1909). Carl Ferdinand's younger sister Margarete Cori (born 1905) was a lecturer of Prague and the wife of the Bohemian Geneticist Felix Mainx (1900, Prague–1983, Vienna).

Carl was the son of Carl Isidor Cori (1865, Brüx (Czech: Most), R.Bohemia, Imp.Austria–1954, Vienna), a Zoologist, and Maria née Lippich (1870, Graz–1922, Prague), a daughter of the Italian-Bohemian/Austrian physician Ferdinand (Franz) Lippich (1838, Padova–1913, Prague).

He grew up in Trieste, where his Father Carl Isidor was the Director of the Marine Biological Station. In late 1914 the Cori family moved to Prague and Carl entered the medical school of Charles University in Prague. While studying there he met Gerty Theresa Radnitz. He was drafted into the Austro-Hungarian Army and served in the ski corps, and later was transferred to the sanitary corps, for which he set up a laboratory in Trieste. At the end of the war Carl completed his studies, graduating with Gerty in 1920. Carl and Gerty married that year and worked together in clinics in Vienna. Their only child, Tom, married Anne, a daughter of the American constitutional Lawyer and anti-feminist Phyllis Schlafy.

Carl was invited to Graz to work with Otto Loewi to study the effect of the vagus nerve on the heart (Loewi would receive the Nobel Prize in Physiology or Medicine in 1936 for this work). While Carl was in Graz, Gerty remained in Vienna. A year later Carl was offered a position at the State Institute for the Study of Malignant Diseases (now the Roswell Park Cancer Institute) in Buffalo, New York and the Cori's moved to Buffalo. In 1928, they became naturalized citizens of the United States.

In addition to winning the Nobel Prize, Cori won the Albert Lasker Award for Basic Medical Research in 1946 and in 1959, the Austrian Decoration for Science and Art. Cori was elected a Foreign Member of the Royal Society (ForMemRS) in 1950 and the Carl Cori Endowed Professorship at Washington University is named in his honor, currently held by Colin Nichols.

Gerty died in 1957 and Carl married Anne Fitz-Gerald Jones in 1960. He stayed on at Washington University until 1966, when he retired as chair of the biochemistry department. He was appointed visiting professor of Biological Chemistry at Harvard University while maintaining a laboratory space at the Massachusetts General Hospital, where he pursued research in genetics. From 1968 to 1983 he collaborated with noted Geneticist Salomé Glüecksohn-Waelsch of the Albert Einstein College of Medicine in New York, until the 1980s when illness prevented him from continuing. In 1976 Carl received the Laurea honoris causa in Medicine from the University of Trieste. Carl shares a star with Gerty on the St. Louis Walk of Fame

While at the Institute the Coris’ research focused on carbohydrate metabolism, leading to the definition of the Cori cycle in 1929. In 1931 Carl accepted a position at the Washington University School of Medicine in St. Louis, Missouri. Carl joined as professor of pharmacology and in 1942 was made professor of biochemistry. In St. Louis, the Cori's continued their research on glycogen and glucose and began to describe glycogenolysis, identifying and synthesizing the important enzyme glycogen phosphorylase. For these discoveries, they received the Nobel Prize in Physiology or Medicine in 1947.