Dabney Coleman was born the youngest of four children in Austin, Texas, on January 3, 1932, to Randolph and Mary Johns Coleman. His father died from pneumonia when Dabney was four years old. He and three older sisters were then raised by his mother in Corpus Christi, Texas. He attended Corpus Christi High School, where he excelled at tennis and became nationally ranked as a junior tennis player.
In 1949, at the age of 17, he enrolled at Virginia Military Institute, where he studied for two years and competed on the school's tennis team. He then attended the University of Texas at Austin for two years, graduating in 1954 with a B.A. in drama. Coleman later recalled that he did not pass many courses and that he was "too busy playing Ping-Pong at the Phi Delta Theta house and calling girls". He was drafted into the United States Army in 1953 and served in West Germany in the Army's Special Services Division for two years. He later told an interviewer, "I spent my military service either playing or teaching tennis." After being discharged by the Army in 1955, he returned to the University of Texas at Austin to enroll in law school.