He matriculated from Magdalen Hall, Oxford, on 9 November 1638, and went in 1639 to New England, where his elder brother, John Woodbridge, had migrated in 1634 in company with his uncle, Thomas Parker and cousin James Noyes.
In 1652 he attempted to refute two ministers of Salisbury, Thomas Warren and William Eyre, in a sermon on Justification by Faith, which was published and commended by Richard Baxter.
Woodbridge published in 1648, under the pseudonym "Filodexter Transilvanus", Church Members set in Joynt, or a Discovery of the Unwarrantable and Disorderly Practice of Private Christians, in usurping the Peculiar Office and Work of Christ's own Pastours, namely Publick Preaching.
He also published in London 1601 a work by James Noyes (who had married his mother's sister), entitled Moses and Aaron; or the Rights of the Church and State.
Woodbridge wrote some verses, inscribed on the tomb of John Cotton of Boston, Massachusetts (d. 1652), which possibly gave Benjamin Franklin a hint for his epitaph upon himself, based on comparison with a book and a new edition.