This was written by Mars Bonfire, which is the stage name of Dennis Edmonton. He wasn't a member of Steppenwolf, but his brother Jerry was the band's drummer.
This was the second single from Steppenwolf's first album. The first single, "Sookie Sookie," was a flop.

TRIVIA:
When Mars Bonfire first introduced  to the song, it was intended as a folk ballad about life on the open road. Once Steppenwolf began working with the song, the tempo was increased, and an iconic rock and roll song resulted.