Johnson began his career as a writer in 1959, penning an episode for U.S. anthology series, Alfred Hitchcock Presents, and also during this time, he sold a short story that would eventually become the basis for 1960 Rat Pack heist film Ocean's 11.

Soon after, he met Twilight Zone creator Rod Serling through a Los Angeles-based writer’s group, and Johnson sold Serling a story which served as the basis for The Twilight Zone episode The Four of Us Are Dying. He went on to pen eight other stories or teleplays for the cult series.

In 1967, he wrote the first-aired episode of iconic sci-fi programme Star Trek, titled The Man Trap, and that same year (67), he collaborated with author William F. Nolan on the dystopian novel Logan's Run.

The book was later adapted into a 1976 film starring Michael York, and a remake is reportedly in the works at Warner Bros.