Hickam is the second son of Homer Hickam, Sr., and Elsie Hickam of Coalwood, West Virginia, United States. He is married to Linda Terry Hickam. His nickname growing up was "Sonny."

Hickam became fascinated with space travel when Sputnik flew over his West Virginia home in 1957. He idolized Wernher von Braun, who headed the United States space program during the 1950s. While in high school, he and his friends (Roy Lee Cook, Quentin Wilson, Sherman Siers, Jimmy "O'Dell" Carroll and Billy Rose) formed the Big Creek Missile Agency and started to build small rockets from spare parts. With support from his chemistry and physics teacher, Freida J. Riley, he graduated from Big Creek High School in 1960. He enrolled at the Virginia Polytechnic Institute (Virginia Tech) and graduated in 1964 with a Bachelor of Science degree in Industrial Engineering. Hickam served for six years with the United States Army, retiring from duty in 1969 as a Vietnam War veteran.

While pursuing a writing career, Hickam worked as an engineer for the United States Army Missile Command from 1971 to 1981. He moved to the National Aeronautics and Space Administration at Marshall Space Flight Center in 1981 as an aerospace engineer. During his career with NASA, Hickam worked in spacecraft design and crew training. His specialties at NASA included training astronauts on science payloads, and extravehicular activities. He trained astronaut crews for many Spacelab and Space Shuttle missions, including the Hubble Space Telescope deployment mission, the first two Hubble repair missions, Spacelab-J, and the Solar Max repair mission. When Hickam retired from NASA in 1998, he was the Payload Training Manager for the International Space Station Program.

On January 15, 2006, Hickam spoke at the memorial service in Buckhannon, West Virginia for 12 miners killed in an explosion at a Sago, West Virginia mine two weeks earlier. The service was televised nationally on CNN.