Moffat was born of humble parentage in Ormiston, East Lothian. He began as a gardener, but in 1814, when employed at the West Hall High Legh in Cheshire, offered himself to the London Missionary Society (LMS). After difficulties with his employers in High Legh due to his Methodist sympathies he found a new interim post at Plantation Farm in Dukinfield where he first met his future wife. In 1816 he was sent out to South Africa and his fiance Mary Smith (1795–1870) followed him 3 years later. After spending a year in Namaqualand, with the chief Afrikaner, whom he converted, Moffat returned to Cape Town in 1819 to marry Mary Smith (1795–1870). She proved to be a remarkable woman and most helpful wife.
In 1820 Moffat and his wife, Mary, left the Cape and proceeded to Griquatown, where their daughter Mary Moffat was born (who was later to marry David Livingstone), and ultimately settled at Kuruman, among the Bechuana tribes living to the west of the Vaal River. Here he worked as a missionary until 1870, when he reluctantly returned finally to his native land. He made frequent journeys into the neighboring regions as far north as the Matabele country. The results of these journeys he communicated to the Royal Geographical Society (Journal 25-38 and Proceedings ii), and when in the United Kingdom of Great Britain and Ireland on furlough (1839–1843) he published his well-known Missionary Labours and Scenes in South Africa (1842). He also translated the whole of the Bible and The Pilgrim's Progress into Setswana.
Moffat was builder, carpenter, smith, gardener, farmer, all in one, and by precept and example he succeeded in turning a "horde of bloodthirsty savages" into a people who could appreciate and cultivate the arts and habits of civilized life, with a written language of their own. He met with incredible discouragement and dangers at first, which he overcame by his strong faith, determination and genial humour. It was largely due to him that David Livingstone, his son-in-law, took up his subsequent work. On his return to England he received a testimonial of 5000 pounds.
His son John Smith Moffat also became an LMS missionary and took over running of the mission at Kuruman before entering colonial service. His grandson Howard Unwin Moffat became a Prime Minister of Southern Rhodesia.
He died at Leigh near Tunbridge Wells, on 9 August 1883, and is buried at West Norwood Cemetery See Lives of Robert and Mary Moffat, by John Smith Moffat (1885); and C. S. Home, The Story of the L. M. S. (1894).
Residents of High Legh organise a Robert Moffat Memorial 10k run beginning and ending at the location of his cottage. http://www.highlegh.org/race.htm