Simpson was born in Jamaica, the son of Rosalind (née Marantz) and Aston Simpson, a lawyer. His father was of Scottish and African ancestry. His mother was born in Russia (Simpson did not find out that she was Jewish until his teenage years). At the age of 17, he emigrated to the United States and began attending Columbia University, where he studied under Mark Van Doren. During World War II, from 1943 to 1945 he was a member of the elite 101st Airborne Division and would fight in France, the Netherlands, Belgium, and Germany. Louis was a runner for the company captain, which involved transporting orders from company headquarters to officers on the front line. His company was involved in a very bloody battle with German forces on the west bank of what is now the Carentan France Marina - Simpson wrote his poem "Carentan" about the experience of US troops being ambushed there. In the Netherlands, he was involved in Market Garden and Opheusden fighting. At Veghel his company suffered 21 killed in a brutal shelling while in the local church yard. At Bastogne bitterly cold temperatures had to be endured while the 101st Division was surrounded by enemy forces for days. After the end of the war he attended the University of Paris. Subsequently, he returned to the US and worked as an editor in New York. He later completed his B.A. at Columbia University's School of General Studies in 1948, and completed his M.A. and Ph.D. at Columbia University in 1950 and 1959, respectively.
His first book was The Arrivistes, published in 1949. It was hailed for its strong formal verse, but Simpson later moved away from the style of his early successes and embraced a spare brand of free verse.
He has taught at universities including Columbia, the University of California-Berkeley, and the State University of New York at Stony Brook. He also briefly taught at The Stony Brook School prior to his retirement. Simpson’s lifelong expatriate status has influenced his poetry, and he often uses the lives of ordinary Americans in order to critically investigate the myths the country tells itself. Although he occasionally revisits the West Indies of his childhood, he always keeps one foot in his adopted country. The outsider's perspective allows him to confront "the terror and beauty of life with a wry sense of humor and a mysterious sense of fate," wrote Edward Hirsch of the Washington Post. Elsewhere Hirsch described Simpson’s Pulitzer Prize–winning collection, At the End of the Open Road, as "a sustained meditation on the American character," noting, "The moral genius of this book is that it traverses the open road of American mythology and brings us back to ourselves; it sees us not as we wish to be but as we are." Collected Poems (1988) and There You Are (1995) focus on the lives of everyday citizens, using simple diction and narratives to expose the bewildering reality of the American dream. Poet Mark Jarman hailed Simpson as "a poet of the American character and vernacular."
Simpson lived on the north shore of Long Island, near Stony Brook. He died on September 14, 2012.