Angell is the son of editor and author Katharine Sergeant Angell White and the stepson of renowned essayist E. B. White, but was raised for the most part by his father, Ernest Angell. He is a 1938 graduate of the Pomfret School and attended Harvard University.

Angell's earliest published works were pieces of short fiction and personal narratives. Several of these pieces were collected in The Stone Arbor and Other Stories (1960) and A Day in the Life of Roger Angell (1970, ISBN 0-670-25916-0).

He first wrote professionally about baseball in 1962, when William Shawn, editor of The New Yorker (for which his mother and stepfather worked from the 1920s through the 1970s), had him travel to Florida to write about spring training.

Since then, Angell has translated a lifetime passion for baseball into a steady stream of elegantly written essays, most of which were originally published in The New Yorker, where he has worked as an editor since 1956. Many of these essays have been collected in a series of critically acclaimed, best-selling books:

A Pitcher's Story (2001, ISBN 0-446-52768-8) is the book-length result of a year that Angell spent speaking with New York Yankees pitcher David Cone and Cone's family, friends and coaches.

Angell has been called the "Poet Laureate of baseball" but dislikes the term. In a review of Once More Around the Park for the Journal of Sport History, Richard C. Crepeau wrote that "Gone for Good," his essay on the career of Steve Blass, "may be the best piece that anyone has ever written on baseball or any other sport."