Born in Portland, Maine, he was educated at Harvard University, where he was friends with American poet, Robert Lowell. Brown dropped out of Harvard after his sophomore year to write poetry, work at Time magazine, and contributed to and became a sub editor of The New Yorker.
Charles Scribner's Sons, of New York, published, in 1941, Brown's sustained unified poem, "The Poem of Bunker Hill". The 158 page poetic epic won praise for its author's literary gifts as a poet and for the timely presentation of a vital topic - young men and war. Louise Bogan, from the New Yorker, was quoted, "Brown...possesses one of the most unmistakable poetic gifts which have recently appeared. Such a talent is not only basically good from the beginning but exhibits, also from the first, all the signs of virtuosity." Also published, early in that year, was Brown's first full-length book, "The End of a Decade".
From the American Revolutionary warfare of "The Poem of Bunker Hill", Harry Brown went directly to modern military operations. Brown enlisted in July 1941 in the US Army Corps of Engineers where he served at Fort Belvoir, Virginia. In 1942 he joined the staff of Yank magazine.
Brown wrote a column for the magazine under the nom de plume of "PFC Artie Greengroin" with a book published in 1945 of the columns under that title. Brown also wrote a play A Sound of Hunting that was produced on Broadway in 1946 starring Burt Lancaster and Frank Lovejoy. It was later filmed by Stanley Kramer under the title Eight Iron Men with a different cast of Bonar Colleano, Lee Marvin, and Arthur Franz in 1952, then was a 1961 television production with Peter Falk, Robert Lansing, and Sal Mineo directed by Seymour Robbie.
Brown wrote the novel A Walk in the Sun in 1944, which was made into a film in 1945. Director Lewis Milestone asked Brown to come to Hollywood as a screenwriter were he worked on films including Sands of Iwo Jima (1949), A Place in the Sun (1951) (winning an Oscar), and Ocean's Eleven (1960). Brown also was credited for his work on the first Ocean's Eleven when it was remade in 2001.