Woodbury was born in Francestown, New Hampshire. He graduated from Dartmouth College in 1809, briefly attended law school in Litchfield, Connecticut, and was admitted to the New Hampshire Bar in 1812.
Woodbury was Justice of New Hampshire state supreme court, 1816-23; Governor of New Hampshire, 1823-24; Speaker of the New Hampshire State House of Representatives, 1825; US Senator from New Hampshire, 1825-31; US Secretary of the Navy under Andrew Jackson, 1831-34; US Secretary of the Treasury under Jackson and Martin van Buren, 1834-41; served again as Senator from New Hampshire, 1841-45; and Justice of the US Supreme Court, 1845-51.
As a US Senator, Woodbury was a dependable Jackson Democrat, and President Jackson appointed him Secretary of the Navy (1831 - 1834) and then Secretary of the Treasury (1834 - 1841). Woodbury successfully worked to end the Second Bank of the United States; like Jackson he favored an "independent" treasury system and "hard money" over paper money. In retrospect, the financial Panic of 1837 and the collapse of speculative land prices were legacies of Woodbury's tenure. After the Panic, Woodbury relized that the US Treasury needed a more secure administration of its own funds than commercial banks supplied, and he backed the act for an "Independent Treasury System" passed by Congress in 1840. It was largely repealed under the new administration the following year, but the foundation was laid for an independent US Treasury, finally established in 1846, under President James K. Polk.
In the 1844 presidential election, Woodbury and the Jackson Democrats supported the Democrats' nomination of Polk. When Polk was elected he promptly named Woodbury an Associate Justice of the US Supreme Court.
Woodbury County, Iowa, was named for him.