Eddy graduated from Shattuck Military School in Faribault, Minnesota, in 1913. He enlisted in the Infantry Branch of the United States Army in 1916 and was commissioned as a second lieutenant of infantry in early 1918, after the American entry into World War I the previous April. With the rank of captain, he was a company commander in the 11th Machine Gun Battalion, part of the 4th Division of the American Expeditionary Force. He was sent to the Western Front with his division in May 1918 and was wounded in August, when the tide of the war had turned against the Germans. He recovered soon after and commanded a machine gun battalion until the end of the war on November 11, 1918.