His father was a lawyer of Scottish descent, and his mother Russian. At 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 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. Louis wrote "Carentan", a poem about the experience where US troops were ambushed. 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, Louis endured bitter cold temperatures while the 101st Division was surrounded by enemy forces for days. After the end of the war he attended the University of Paris.
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 received a Ph.D. from Columbia and taught there, as well as University of California, Berkeley, and the State University of New York at Stony Brook.
He currently lives on the north shore of Long Island near Stony Brook.