Fulton was born in Manhattan, New York, on April 15, 1909, and named for Thomas Edison, who was a friend of his father, Robert Fulton Sr., a president of Mack Trucks. His maternal grandfather, Ezra Johnson Travis, ran stagecoach lines across the old west after the Civil War, and his uncle, Elgin Travis, who took them over from his father, eventually converted the stagecoach routes into bus lines, which became Greyhound Bus Line. As a teenager, he was in the elite when he traveled by commercial aircraft from Miami, Florida, to Havana, Cuba, in 1921, and then to Egypt when Tutankhamun's tomb was opened in 1923. He attended middle school at Le Rosey in Lausanne, Switzerland, for two years, then went to Exeter and Choate, graduated with a degree in architecture from Harvard in 1931, and spent a further year of architectural study in Vienna at the University of Vienna. At age 23, he traveled 25,000 miles (from London to Tokyo in 18 months) on a twin-cylinder Douglas motorcycle to study architecture around the world. Along the way, he shot 40,000 feet of film of his travels, over the 18-month period.