Woodbury moved to Washington, D.C., with his parents when he was ten. He attended a select academy there instituted by Salmon P. Chase. He attended Columbia College and the Catholic College in Georgetown, graduating from the latter school at an early age. He then began studying law, first in the office of United States Attorney GeneralBenjamin F. Butler and then with Roland S. Coxe. He was admitted to the bar before he turned twenty. He moved to Lowndes County, Alabama, shortly after he was admitted to the bar and practiced law there. He moved to Boston in 1845 and practiced law there. He initially practiced law with future congressman Robert Rantoul Jr. for a few years. He then practiced law largely on his own, although he occasionally associated with younger lawyers, including Charles G. Chick and Josiah P. Tucker in his later years.[2] In the earlier days of his law practice, he jointly edited with George Minot the three-volume Reports of Cases argued and determined in the Circuit Court of the United States for the First District, which contained his father's decisions as judge from 1847 to 1852. He also edited the second and third volume of Levi Woodbury's Writings and wrote pamphlets on the fisheries question and other matters related to diplomatic relations between the United States and Canada.[3]
Woodbury was a member of the New England Historic Genealogical Society from 1867 until his death. He also served as its vice-president in 1895, and in 1897 he drafted a bill that authorized the admission of women as members of the Society.[5] He was also an honorary member of the Maine Historical Society and the New Hampshire Historical Society. He was involved with the Freemasons and held high offices in the York Rite and Scottish Rite, serving as second officer and on the supreme council of the latter body. He was also a trustee for the Grand Lodge of Massachusetts and was on the board for the supreme council.[9]