Boyce was born in Grays Inn Terrace in London, and was the son of George Boyce, a wine merchant turned pawnbroker. He went to school in Chipping Ongar in Essex, and then studied in Paris. In October 1843 he was articled to an architect named Little, with whom he remained for four years, until joining the architectural firm of Wyatt and Brandon. Already disillusioned with architecture a meeting with the artist David Cox in August 1849 persuaded him to give up the profession and take up watercolour painting instead.
His early work shows the influence of Cox who he met again in Bettws-y-Coed in 1851, but he went on to develop his own detailed style under the influence of the Pre-Raphaelite painters, having met Thomas Seddon and Rossetti in about 1849 and William Holman Hunt and John Everett Millais in 1853, in which year he painted in Dinan, Brittany, with Seddon. In 1854 he went to Venice, where he sketched subjects recommended to him by the critic John Ruskin. who corresponded with him during his four months in the city.