Waterston's father, George, was an Edinburgh sealing wax manufacturer and stationer, a relative of the Sandeman family Robert and his brother, George. John was born, the sixth of nine children, into a family alive with interests in literature, science and music. He was educated at Edinburgh High School before becoming apprenticed as a civil engineer to Messrs. Grainger and Miller. His employers encouraged him to attend lectures at the University of Edinburgh. He studied mathematics and physics under Sir John Leslie as well as attending lectures in chemistry, anatomy and surgery and becoming an active participant in the student literary society.