Roberts was born in Groes, Denbighshire, Wales to William Roberts, a farmer. Although he spent some years of his childhood there, he later moved to Liverpool. There, he became an apprentice to John Johnson & Son (which later became Johnson and Robinson), a firm of mechanical engineers, for 7 years beginning on 12 November 1844. He became a partner in 1847, and supplemented his job with night school. When Peter Robinson died in 1855, Roberts was made manager of the firm. When the other partner, John Johnson died, Roberts was in charge of the contracts and affairs of the firm. Roberts began working as a builder in 1859, and was joined by Peter Robinson's son, J. J. Robinson, in 1862. He was very successful, and became known as one of the best engineers in the region.