Born in Jamaica Plain outside of Boston, Massachusetts, Wheelwright completed an A.B. from Harvard College in 1906 and an M.L.A. from Harvard University in 1908. In 1910, he went to work for Charles Downing Lay, a founding member of the American Society for Landscape Architects. That same year he established Landscape Architecture, the quarterly journal of the ASLA with Harvard professor Henry Vincent Hubbard. Wheelright served as editor of the publication until 1920. His time at the journal was interrupted in 1917 when he served in World War I as a planner for Camp Dodge, Iowa, and Camp Merritt, New Jersey. From 1919 to 1923, he practiced independently, moving from New York to Philadelphia where he established the Department of Landscape Architecture at the University of Pennsylvania in 1924, teaching until 1941.
In 1926, Wheelwright opened a firm with Markley Stevenson in Philadelphia and went on to design gardens for the private estates Valley Garden and Goodstay, Wilmington, Delaware; Pierce House, Bryn Mawr, Pennsylvania; and Spite House, Rockport, Maine, the latter two of which exemplify his prolific use of the Colonial Revival style. While estates remained his focus, Wheelwright designed a public housing project in Wayne, Pennsylvania, Fort Christina Park in Wilmington, Delaware, and the World War II cemetery, St. Laurent, along Omaha Beach in Normandy, France.