He was born Robert Creel Davis in Tallahassee, Florida to Eugene Davis (a dentist whose career declined due to alcoholism) and his wife, Anne (née Creel) Davis. His brother Gene is also an actor. According to an article in The New York Times published in 1987, Davis suffered physical abuse and sexual abuse at the hands of both parents. As an adult, he was an alcoholic and an intravenous drug user before becoming sober in 1981. Davis was known as “Bobby” during his youth, but took Brad as his stage name in 1973.  At 16, after winning a music-talent contest, Davis worked at Theater Atlanta. He later moved to New York City and attended the American Academy of Dramatic Arts, as well as studied acting at the American Place Theater. After a role on the soap opera How to Survive a Marriage, he performed in Off-Broadway plays.  In 1976, he was cast in the television mini-series Roots, then as Sally Field’s love interest in the television film Sybil. In 1981 he played American track star Jackson Scholz in the Academy Award winning film Chariots of Fire. He played the lead role in Larry Kramer’s play about AIDS, The Normal Heart (1985). His most successful film role was as the main character, Billy Hayes, in Midnight Express (1978), for which he won the Golden Globe Award for New Star of the Year – Actor and the Golden Globe Award for Best Motion Picture Acting Debut – Actor. He was also nominated for a similar award at that year’s BAFTA Awards, in addition to receiving Best Actor nominations at both ceremonies.

Davis married Susan Bluestein, an Emmy Award-winning casting director. They had one child, Alex, a transgender man born as Alexandra. Davis acknowledged having had sex with men and being bisexual in an interview with Boze Hadleigh.  Diagnosed with HIV in 1985, Davis kept his condition a secret until shortly before his death at age 41, on September 8, 1991 in Los Angeles. It was revealed in a book proposal that Davis had written before his death that he had to keep his medical condition a secret in order to be able to continue to work and support his family.  Although the announcement said he died of AIDS, he actually died of an intentional drug overdose. Near death and in severe pain in a hospital, he opted to end his life on his own terms. With his wife and a family friend present, he committed assisted suicide. Susan Davis continues to campaign to combat AIDS.