Born near Three Rivers, Michigan, Godshalk earned a master’s degree in landscape design from the University of Michigan in 1921. He was then hired as the foreman of construction for the Morton Arboretum in Lisle, Illinois (outside of Chicago), having been alerted to the position by O.C. Simonds. Godshalk was appointed superintendent of the arboretum in 1922, and he implemented Simonds’ design of naturalistic scenery interspersed with winding paths, open lawns, and meadows—a setting that would serve as both public park and laboratory for botanical research.
Godshalk became director of the arboretum in 1934, a post he would occupy for 32 years. In 1962 he developed plans to restore some 50 acres of eastern tallgrass prairie on land previously acquired along the arboretum’s western border—one of the earliest prairie restoration projects in the Midwest. When he retired from the Morton Arboretum in 1966, he was named director emeritus. He then served as a consultant to a 45-acre arboretum being developed at Fernwood Botanical Garden and Nature Preserve in Niles, Michigan, and he played a key role in establishing the Hawthorn Hollow Arboretum in Kenosha, Wisconsin. He received the Arthur Hoyt Scott Horticultural Medal from Swarthmore College’s Scott Arboretum, the Thomas Roland Medal from the Massachusetts Horticultural Society, and the Johnny Appleseed Medal from the Men's Garden Clubs of America. In 1940 he was instrumental in organizing the American Association of Botanical Gardens and Arboretums, serving as its second president. Godshalk died while hospitalized in the Chicago suburb of Naperville at the age of 91.