Woodbury's interest in art was evident at an early age, for he is said to have taught himself to draw at the age of five and to paint by the age of ten. From 1882 to 1886, Woodbury studied mechanical engineering at M.I.T. He began painting marines of the coastal area around Boston and attending evening life classes at the Boston Art Club while still in college. After his graduation in 1886, Woodbury opened a studio in Boston.
In 1888, Woodbury began executing illustrations for magazines including Century and Harper's. He also taught a painting class in his studio. He married the painter Marcia Oakes in 1890. He was in Belgium, Holland, Germany, Italy and Switzerland, before enrolling at the Academie Julian in Paris for four months, studying with Gustave Boulanger and Jules Joseph Lefevbre. Woodbury visited Katwijk, Holland during the summer of 1891.
Although he returned to Boston during the fall of 1891, Woodbury was frequently in Europe for almost the next twenty years. He often staying at the small coastal villages like Laren and Volendam in Holland, painting scenes of Dutch peasant life. However, marines continue to predominate in Woodbury's work. Inspired by the violent and dramatic North Sea off Holland, he often sailed with local fisherman, studying the movement of the currents and waves.
Like the North Sea, the rugged shores and turbulent waves of the Atlantic coastline provided Woodbury with another setting for his seascapes. He built a studio in Ogunquit, Maine in 1896, where he began teaching summer school two years later. Woodbury's classes continued annually until 1915 and resumed during the years from 1923 to 1939. Additionally, Woodbury taught at Wellesley College from 1899 to 1906 and again from 1913 to 1914, and lectured nationally, including at Dartmouth College and the Art Institute of Chicago.
After the turn of the century, Woodbury began visiting warmer coastal regions of the Caribbean in search of settings for his works. He made several trips to Jamaica and from the later years of the twenties until his death, he was in the islands almost yearly, especially at Trinidad and British Guiana. Financially very successful, Woodbury was a member of numerous art organizations and the author of several books on art. Following his death, the Academy cited Woodbury as a "man of exceptional versatility, . . . a well-known marine painter and etcher" (CM, April 24, 1940).
He became an Associate through merger with SAA.