Waugh was the first son of General Gilbert Waugh who served as military auditor-general in Madras. After studying at Edinburgh he joined Addiscombe Military Seminary in 1827 and was commissioned with the Bengal Engineers on 13 December of the same year. He trained at Chatham where he studied under Sir Charles Pasley before reaching India in May 1829. He assisted Captain Hutchinson in establishing a foundry at Kashipur and became an adjutant of the Bengal sappers and miners on 13 April 1831. In 1832 he was posted to the Great Trigonometrical Survey under George Everest. Waugh surveyed many parts of central India before moving to the headquarters in Dehra Dun. Everest noted that Waugh and Renny were the best in mathematical skills and in the handling of instruments.