Brandon was born in Kokomo, Indiana, but spent his childhood in various locales, including the Yucatán and New Mexico. He began working as a professional writer in 1938, although this was interrupted by his service as a photographer for the United States Army Air Forces in the Pacific Theater during World War II.
During his long career Brandon published a variety of short fiction, essays, and poetry, which appeared in magazines such as Esquire, The Atlantic Monthly, The Paris Review, The Saturday Evening Post, and Reader's Digest. However, he is best known for his historical work documenting Native Americans and the American West. Although Brandon's formal education ended after high school, his scholarship was sufficiently respected that he was from 1966–1967 a visiting professor at the University of Massachusetts, and later conducted a seminar series on Native American literature at California State College in Long Beach, California.