He received a Bachelor of Science degree from Harvard University in 1924.
He was in private practice of law in Manchester, New Hampshire, from 1927 until the early 1930s.
Woodbury was nominated by President Franklin D. Roosevelt on January 31, 1941, to a seat on the United States Court of Appeals for the First Circuit vacated by Judge Scott Wilson.
On December 7, 1960, Woodbury was injured when the train he was traveling on collided with a bottled gas truck.
[1] Six people were killed in the accident, one of whom was Woodbury's law clerk at the time.