Robert was born in Willington Quay, on the Northumberland coast, the son of George Stephenson and his wife, Frances Henderson. The family moved to Killingworth, where Robert was taught at the local village school. Robert attended the middle-class Percy Street Academy in Newcastle and at the age of fifteen was apprenticed to the mining engineer Nicholas Wood. He left before he had completed his three years to help his father survey the Stockton and Darlington Railway. Robert spent six months at Edinburgh University before working for three years as a mining engineer in Colombia. When he returned his father was building the Liverpool and Manchester Railway, and Robert developed the steam locomotive Rocket that won the Rainhill Trials in 1829. He was appointed chief engineer of the London and Birmingham Railway in 1833 with a salary of £1,500 per annum. By 1850 Robert had been involved in the construction of a third of the country's railway system. He designed the High Level Bridge and Royal Border Bridge on the East Coast Main Line. With Eaton Hodgkinson and William Fairbairn he developed wrought-iron tubular bridges, such as the Britannia Bridge in Wales, a design he would later use for the Victoria Bridge in Montreal, for many years the longest bridge in the world. He eventually worked on 160 commissions from 60 companies, building railways in other countries such as Belgium, Norway, Egypt and France.
In 1829 Robert married Frances Sanderson who died in 1842; the couple had no children and he did not remarry. In 1847 he was elected Member of Parliament for Whitby, and held the seat until his death. Although Robert declined a British knighthood, he was decorated in Belgium with the Knight of the Order of Leopold, in France with the Knight of the Legion of Honour and in Norway with the Knight Grand Cross of the order of St. Olaf. He was elected a Fellow of the Royal Society (FRS) in 1849. He served as President of the Institution of Mechanical Engineers and Institution of Civil Engineers. Robert's death was widely mourned, and his funeral cortège was given permission by Queen Victoria to pass through Hyde Park, an honour previously reserved for royalty. He is buried in Westminster Abbey.