Horner was born in Los Angeles in 1953, the son of Joan Ruth (Frankel) and Harry Horner, who was a set designer and occasional art-director. He had a brother, Christopher, who is a writer and documentary filmmaker. His family was Jewish. His mother was from Canada, and his father, who was born in Holíč, Czechoslovakia, moved to the United States in 1935.

Horner started playing piano at the age of five. His early years were spent in London, where he attended the Royal College of Music. He returned to America where he attended Verde Valley High School in Sedona, Arizona, and later received his bachelor's degree in music from the University of Southern California. After he earned a master's degree, he started work on his doctorate at the University of California, Los Angeles (UCLA), where he studied with Paul Chihara, among others.

After several scoring assignments with the American Film Institute in the 1970s, he finished teaching a course in music theory at UCLA and subsequently turned to film scoring. Horner was also an avid pilot.