[2] Drew was born in 1904 into an African-American middle-class family in Washington, D.C.[3] His father, Richard, was a carpet layer[4] and his mother, Nora Burrell, trained as a teacher.

[6] From 1920 until his marriage in 1939, Drew's permanent address was in Arlington County, Virginia,[7] although he graduated from Washington's Dunbar High School in 1922 and resided elsewhere during that period of time.

[5][8] Drew won an athletics scholarship to Amherst College in Massachusetts,[9] where he played on the football as well as the track and field team, and later graduated in 1926.

[12] It was during this stage in his medical journey that Drew worked with John Beattie, who was conducting research regarding the potential correlations between blood transfusions and shock therapy.

[13] Shock occurs as the amount of blood in the body rapidly declines which can be due to a variety of factors such as a wound or lack of fluids (dehydration).

[14] He then joined Freedman's Hospital, a federally operated facility associated with Howard University, as an instructor in surgery and an assistant surgeon.

In 1938, Drew began graduate work at Columbia University in New York City on the award of a two-year Rockefeller fellowship in surgery.

[12][16] The District of Columbia chapter of the American Medical Association allowed only white doctors to join, consequently "... Drew died without ever being accepted for membership in the AMA.

"[17] In late 1940, before the U.S. entered World War II and just after earning his doctorate, Drew was recruited by John Scudder to help set up and administer an early prototype program for blood storage and preservation.

[19] In 1939, Drew married Minnie Lenore Robbins, a professor of home economics at Spelman College in Atlanta, Georgia, whom he had met earlier during that year.

Despite a popular myth to the contrary, once repeated on an episode ("Dear Dad... Three") of the hit TV series M*A*S*H and in the novels Carrion Comfort and The 480, Drew's death was not the result of his having been refused hospital access because of his race.

[24][25][26] This myth spread, however, because it was not then uncommon for black people to be refused treatment because there were not enough "Negro beds" available or the nearest hospital only serviced whites.

[27] Numerous schools and health-related facilities, as well as other institutions, have been named in honor of Drew, including the Martin Luther King Jr./Drew Medical Center in Los Angeles.