Cooley was born in August 22, 1920 in Houston and graduated in 1941 from the University of Texas at Austin (UT), where he was a member of the Kappa Sigma fraternity and the Texas Cowboys, played on the basketball team, and majored in zoology. He became interested in surgery through several pre-medical classes he attended in college and began his medical education at the University of Texas Medical Branch in Galveston. He completed his medical degree and his surgical training at the Johns Hopkins School of Medicine in Baltimore, Maryland, where he also completed his internship. At Johns Hopkins, he worked with Dr. Alfred Blalock and assisted in the first "Blue Baby" procedure to correct an infant's congenital heart defect.

Cooley's interests included basketball, which he played in high school and as a three-year letterman for the UT men's basketball team (1939–1941), and golf, which he became interested in during his youth and played for 68 years. (The practice and training facility of the UT men's and women's basketball teams — the Denton A. Cooley Pavilion, which opened in 2003 — was named in his honor.) Among his other outside interests, Cooley played upright bass in a swing band called The Heartbeats from 1965 through the early 1970s.

In 1946 Cooley was called to active duty with the Army Medical Corps. There, he served as chief of surgical services at the station hospital in Linz, Austria, and was discharged in 1948 with the rank of captain. He then returned to complete his residency at Johns Hopkins and remain as an instructor in surgery. In 1950 he went to London to work with Russell Brock.

In the 1950s Cooley returned to Houston to become associate professor of surgery at Baylor College of Medicine and to work at its affiliate institution, The Methodist Hospital. During the 1950s, Cooley began working with American cardiac surgeon, scientist, and medical educator Michael E. DeBakey. During that time he worked on developing a new method of removing aortic aneurysms, the bulging weak spots that may develop in the wall of the artery.

His skill as a surgeon was demonstrated as he successfully performed numerous bloodless open-heart surgeries on Jehovah's Witnesses patients beginning in the early 1960s.

He and his colleagues worked on developing new artificial heart valves from 1962 to 1967; during that period, mortality for heart valve transplants fell from 70% to 8%. In 1969, he became the first heart surgeon to implant an artificial heart designed by Domingo Liotta in a man, Haskell Karp, who lived for 65 hours. The next year, in 1970, "he performed the first implantation of an artificial heart in a human when no heart replacement was immediately available."

On March 13, 1972, the Denton A. Cooley Cardiovascular Surgical Society was founded at the Texas Heart Institute by the Residents and Fellows of Cooley to honor him. Founding President Philip S. Chua had envisioned this exclusive Society to foster academic, professional and personal camaraderie among cardiac Surgeons in the United States and around the world through scientific seminars and symposia. There are now more than 900 cardiac Surgeons from more than 50 countries around the globe who are members of the Denton A. Cooley Cardiovascular Surgical Society.In the HBO film Something the Lord Made, Cooley was portrayed by Timothy J. Scanlin, Jr.

Cooley filed for bankruptcy in 1988, citing real estate debts during a market downturn.

During the 2000 U.S. presidential election, Cooley was asked by then-candidate George W. Bush to review vice-presidential candidate Dick Cheney's medical records, particularly concerning the status of his chronic heart condition.

Cooley and the heart surgeon Michael E. DeBakey had a professional rivalry that lasted more than 40 years. They made amends in a public rapprochement on November 7, 2007, when DeBakey was 99 years old (Cooley was 87). Cooley died on November 18, 2016, at the age of 96.