Leitch began his career as an apprentice to a sign painter in Glasgow. In 1824, he became a scene painter at the Glasgow Theatre Royal, a trade he continued after his move to London in 1830. It was in London that he began to produce watercolors and oil paintings. While in his twenties, Leitch traveled to Italy where he stayed for several years, returning with a large collection of sketches and finished watercolors, extensive teaching experience, and numerous introductions to aristocratic families. Starting in 1842 and continuing for a period of 22 years, Leitch gave drawing and watercolor lessons to Queen Victoria and members of the royal family. After being declined admission to the Society of Painters in Water-Colours, Leitch was invited to join the New Water-Colour Society in 1862, becoming a prominent contributor to that society's annual exhibitions and serving as its vice-president from 1873 until his death.