He graduated from the University of Vermont in 1840.
He served as a United States. Representative from Vermont. He began the practice of law in Vergennes. Woodbridge was the mayor of Vergennes for five years, and was the Vermont Auditor of Accounts from 1850 until 1852.
He was a prosecuting attorney from 1854 to 1858.
He engaged in the construction of railroads and was vice-president of the Rutland and Washington Railroad. Woodbridge served in the Vermont Senate in 1860 and 1861, serving as president pro tempore in the latter year.
Woodbridge was elected a Republican candidate to the United States House of Representatives in 1862, serving from 1863 to 1869. He was a major proponent of the Expatriation Acting of 1868.
After leaving Congress, he resumed practicing law until his death in Vergennes, Vermont on April 25, 1888.
He is interred in Prospect Cemetery in Vergennes.
He served as a member of the Vermont House of Representatives in 1849, 1857 and 1858.