McClatchy was born in Bryn Mawr, Pennsylvania, in 1945. He was educated at Georgetown and Yale, from which he received his Ph.D. in 1974. He lives in Stonington, Connecticut and New York. His partner is graphic designer Chip Kidd.
McClatchy is an adjunct professor at Yale University and editor of the Yale Review. He also edits the "Voice of the Poet" series for Random House AudioBooks.
His book Hazmat (Alfred A. Knopf, 2002) was nominated for the 2003 Pulitzer Prize. He has written texts for musical settings, including eight opera libretti, for such composers as Elliot Goldenthal, Daron Hagen, Lowell Liebermann, Lorin Maazel, Tobias Picker, Ned Rorem, Bruce Saylor, and William Schuman. His honors include an Award in Literature from the American Academy of Arts and Letters (1991). He has also been one of the New York Public Literary Lions, and received the 2000 Connecticut Governor’s Arts Award.
In 1999, he was elected into the membership of The American Academy of Arts and Letters, and in January 2009 he was elected president. He is a Fellow of the American Academy of Arts and Sciences and has received fellowships from the Guggenheim Foundation (1987), the National Endowment for the Arts, and the Academy of American Poets (1991). He served as Chancellor of the Academy of American Poets from 1996 until 2003.
With UCLA professor and poet Stephen Yenser, McClatchy serves as co-executor for the literary estate of James Merrill (1926-1995).