Having graduated from Yale with a B.A. in 1973 and a Ph.D four years later, he became an instructor at Princeton University, where he was promoted to Mellon Professor of English before returning to Yale in 1988. In 1995 he was appointed as Housum Professor of English at Yale. In 2006 he became a Sterling Professor.
Bromwich is a fellow of the American Academy of Arts and Sciences. He has published widely on Romantic criticism and poetry, and on eighteenth-century politics and moral philosophy. His book Politics by Other Means concerns the role of critical thinking and tradition in higher education, and defends the practice of liberal education against political encroachments from both Left and Right. His essays and reviews have appeared in The New Republic, The New York Review of Books, the London Review of Books, TLS, and many other U.S. and British journals. He is a frequent contributor of political blog posts on the Huffington Post.
Bromwich's Skeptical Music was awarded the PEN/Diamonstein-Spielvogel Award for the Art of the Essay in 2002.
Bromwich argued forcefully against American intervention in the Syrian conflict. He has been a frequent critic of the Obama administration's caution and failure to achieve more of the Democratic party's policy agenda. He criticized the 2011 State of the Union Address for a lack of focus on gun control and immigration and for rhetorical concessions to conservative ideology. In 2014, he criticized the "disengagement" of the administration, saying that President Obama "watches the world as its most important spectator."
- The Intellectual Life of Edmund Burke: From the Sublime and Beautiful to American Independence (Cambridge, MA: Belknap Press, 2014).
- Moral Imagination: Essays (Princeton, NJ: Princeton University Press, 2014).
- American Sonnets: An Anthology (New York, NY: Library of America, 2007). Editor.
- On Liberty (New Haven, CT: Yale University Press, 2003). By John Stuart Mill. New edition with a biographical essay by David Bromwich, an interpretative essay by George Kateb, and commentaries by various authors.
- Skeptical Music: Essays on Modern Poetry (Chicago, IL: University of Chicago Press, 2001).
- On Empire, Liberty, and Reform: Speeches and Letters of Edmund Burke (New Haven, CT: Yale University Press, 2000). Editor.
- Hazlitt: The Mind of a Critic (Oxford: Oxford University Press, 1983; 2nd ed. 1999).
- Disowned by Memory: Wordsworth's Poetry of the 1790s (Chicago, IL: University of Chicago Press, 1998).
- Politics by Other Means: Higher Education and Group Thinking (New Haven, CT: Yale University Press, 1992).
- A Choice of Inheritance: Self and Community from Edmund Burke to Robert Frost (Cambridge, MA: Harvard University Press, 1989).
- Romantic Critical Essays (Cambridge English Prose Texts) (Cambridge: Cambridge University Press, 1988). Editor.
- "David Bromwich appointed Sterling Professor of English". Yale Bulletin & Calendar 34 (29). May 19, 2006. Retrieved 2014-06-28.
- "English Dept. Faculty & Staff » David Bromwich". english.yale.edu. Retrieved 13 June 2013.
- "2002 Literary Awards Winners". PEN. Retrieved 2014-06-28.
- David Bromwich (2013). "Stay Out of Syria!". The New York Review of Books 60 (11). Retrieved 23 June 2013.
- Bromwich, David (January 28, 2011). "Obama, Incorporated". New York Review of Book Blog. Retrieved 2014-06-28.
- Bromwich, David (3 July 2014). "The World’s Most Important Spectator". London Review of Books 36 (13): 3–6. Retrieved 2014-06-28.