Livingstone was born on 19 March 1813 in the mill town of Blantyre, Scotland, in a tenement building for the workers of a cotton factory on the banks of the River Clyde under the bridge crossing into Bothwell. He was the second of seven children born to Neil Livingstone (1788–1856) and his wife Agnes (née Hunter; 1782–1865). David was employed at the age of ten in the cotton mill of Henry Monteith & Co. in Blantyre Works. He and his brother John worked twelve-hour days as piecers, tying broken cotton threads on the spinning machines.