Born in Camden, New Jersey, Stevenson received a degree in civil engineering from Lafayette College in Easton, Pennsylvania, and an M.L.A. from Harvard University in 1923. Upon graduating, he went to work for Olmsted Brothers, leaving that firm to work with Robert Wheelwright in 1928. In the 1930s, Stevenson served as the National Park Service's regional inspector for Philadelphia, becoming a consultant to the Pennsylvania Bureau of Parks in 1936. During WWII, he became chief of a site planning unit in the War Department. He and Wheelwright established the firm Stevenson and Wheelwright in 1948, and Stevenon served as a consultant to the American Battle Monuments Commission that same year. His designs include the American Cemetery at Normandy, the U.S. Marine Corps War Memorial in Virginia, and the Daniel Boone Homestead in Pennsylvania. Stevenson was a consulting landscape architect to Princeton University for three years beginning in 1958. Along with his design work, Stevenson wrote and taught classes in horticulture. His publications included Why We Need Parks and a Survey and Report of Recommendations for a Comprehensive State Park System for Pennsylvania. He was elected a Fellow of the American Society of Landscape Architects in 1946, and later served as its president.