Alexander was born in Haymarket, Virginia and an 1823 graduate of the United States Military Academy at West Point, New York – along with Lorenzo Thomas, Alfred Mordecai and George S. Greene. He was a cadet at the Military Academy, Oct. 6, 1818, to July 1, 1823, when he was graduated and promoted in the Army to Brevet Second Lieutenant in the 6th Infantry. He was shortly after promoted to Second Lieutenant in the 3d Infantry with the same date of rank. He served on frontier duty at Fort Atkinson, Council Bluffs, Iowa, 1824; in garrison at Detroit, Mich., 1824‑25, — Green Bay, Wis., 1825‑26; Jefferson Barracks, Mo., 1826‑27; and Ft. Armstrong, Ill., 1828‑29; on Recruiting service, 1829‑30; on frontier duty at Jefferson Barracks, Mo., 1830; and at Natchitoches, Louisiana, 1830‑31. He served at Fort Towson, in the Indian Territory from 1831 to 1835; on Quartermaster duty at Fort Towson, I. T., 1833‑34, Fort Jesup, Louisiana, 1834‑35, Ft. Towson, I. T., 1835, Ft. Jesup, La., 1835‑38, Fort Smith, Ark., 1839, Ft. Towson, I. T., 1840, Ft. Jesup, La., 1840, Ft. Towson, I. T., 1840. He served at Fort Smith, Arkansas from 1840 to 1846, during which he was briefly assigned to Washington, D. C. in 1844.
Assault and Capture of the City of Mexico, Sep. 13‑14, 1847
After the War with Mexico was concluded he was in garrison at Jefferson Barracks, Mo., 1848‑49; on frontier duty, on march to New Mexico, 1849, Santa Fé, N. M., 1849‑50, Las Vegas, N. M., 1850‑51, Ft. Union, N. M., 1851‑52, Ft. M'Kavett, Tex., 1853 and the march to El Paso in late 1853. Alexander, as a brevet Lieutenant Colonel, led the 8th Infantry, when it became the first garrison stationed at Fort Bliss in the El Paso, Texas, area, from January 1854 through March 1855. In March 1855, promoted to Colonel, Alexander was appointed as commander of the new 10th Infantry. He later led his regiment in the Utah War. He served in garrison at Carlisle Barracks, Pa., 1855; on frontier duty at Fort Snelling, Minnesota from 1855 to 1856; Fort Ridgely, Minnesota, 1856‑57, and the Utah Expedition, 1857 to 1858. He was on a leave of absence from 1858 to 1860.
Civil War
Alexander was on frontier duty at Fort Laramie, Dakota Territory from 1860 to 1862. He then transferred to Fort Kearny, Nebraska, where he served until 1863. Alexander served during the American Civil War as Acting Assistant Provost Marshal General, Superintendent of Volunteer Recruiting Service, and Chief Mustering and Disbursing Officer for the State of Missouri, with headquarters at St. Louis from May 1, 1863, to Apr. 25, 1866.
Post war
After the war, he was in command of 10th Infantry at Fort Snelling, Minnesota from May, 1866 until he retired from active service on February 22, 1868, under the Law of July 17, 1862, as he was over "the Age of 62 Years." General Alexander died on January 3, 1888, at Washington, D. C. at the age of 85. He was buried in Oakland Cemetery in St. Paul, Minnesota.
Promotions
Second Lieutenant, 3d Infantry – July 1, 1823
First Lieutenant, 3d Infantry – December 29, 1827
Assistant Quartermaster – December 6, 1833, to July 7, 1838
Captain, Staff, Assistant Quartermaster – July 7, 1838 to June 18, 1846
Captain, 3d Infantry – July 7, 1838
Brevet Major – Apr. 18, 1847
Brevet Lieut.‑Colonel - Aug. 20, 1847
Major, 8th Infantry – November 10, 1851
Colonel, 10th Infantry – March 3, 1855
Brevet Brigadier General – October 18, 1865
Namesake
In World War II, a United States Army transport ship,, was named in his honor.
