Craig was born on August 5, 1875 in Saint Joseph, Missouri. He entered the United States Military Academy at West Point, New York on June 20, 1894.
Craig graduated from West Point on April 26, 1898 and was commissioned as a second lieutenant in the Infantry branch. He transferred to the Cavalry on June 23 and served with the 6th Cavalry.
He served in the China Relief Expedition and in the Philippine Insurrection. He was promoted to first lieutenant on February 2, 1901 and to captain on May 7, 1904.
After serving in the Spanish–American War, Philippine–American War, and the relief expedition during the Boxer Rebellion, Craig attended the Infantry and Cavalry School from 1903 to 1904 and the Staff College from 1904 to 1905. He was then promoted to captain and served in the 10th and 1st cavalry regiments, and was garrisoned as a regimental quartermaster at Fort Clark in Kinney, Texas from 1906 to 1909. He would go on to graduate from the Army War College in 1910 and serve in a variety of administrative positions, most notable of which was assigning troops to their regiments. He would then serve with the 1st Cavalry Regiment of the western U.S. in 1912, then became an instructor at Fort Leavenworth located in Leavenworth, Kansas in 1916 until 1917 where he was moved to the General Staff Corps.
Craig was promoted to major on May 15, 1917 shortly after the United States entered World War I in April of the same year. He was promoted to temporary lieutenant colonel on August 17 and temporary colonel on March 27, 1918.
He served in France during World War I as chief of staff to General Hunter Liggett in the 41st Infantry Division and later in I Corps where he was promoted to temporary brigadier general on July 11, 1918. He then became chief of staff of the 3rd Army.
He received the Distinguished Service Medal for his service during the First World War. His citation reads as follows:
General Craig served in turn as Chief of Staff of a division, a corps, and an Army, in each of which capacities he exhibited great ability. His personal influence, aggressiveness, and untiring efforts were repeatedly displayed in the operations of the 1st Corps in the vicinity of Chateau-Thierry, on the Oureq, and the Vesle during the St. Mihiel and Argonne-Meuse offensives.
After the war, Craig reverted to his permanent rank of major on August 15, 1919 but was promoted to colonel on July 1, 1920 and to brigadier general only 15 days later.
When Craig was promoted to colonel, he was put in command of the District of Arizona in 1920 and became the commandant of the Cavalry School from 1921 to 1923 after his promotion to brigadier general in April 1921.
He served as Chief of Cavalry with the rank of major general from July 24, 1924 to March 20, 1926. He also commanded the Panama Canal Zone.
Craig served as president of the Army War College in 1935 and served as the U.S. Army Chief of Staff from October 2, 1935 to August 31, 1939, succeeding General Douglas MacArthur, and preceding George C. Marshall. That appointment carried with it a temporary promotion to full (four star) general.
As Chief of Staff of the Army, Craig pointed out to Congress the Army's lack of preparedness in manpower and material, stressed the necessity of lead time in military preparedness, focused attention on Army planning, and, within governmental constraints, prepared the Army for World War II. He retired, in his permanent rank of major general, on August 31, 1939 - after forty-one years of active duty. Upon his retirement, he received a second Distinguished Service Medal for his service as Army Chief of Staff.
General Craig's retirement was short-lived, however. On September 26, 1941, with war on the horizon he was recalled to active duty to head the War Department's Personnel Board, a body responsible for selecting individuals who were to receive direct commissions in the army. He headed the board in his permanent rank of major general until shortly before his death.
He died at the Walter Reed Hospital in Washington, D.C. on July 25, 1945, where he had been ill for the previous year. He was posthumously awarded a third Distinguished Service Medal and was buried in Arlington National Cemetery.