Wright was born in Purdy, Tennessee. He was admitted to the bar, and practiced at Memphis.
In 1861, Wright was ordered to establish a fortification at Randolph, Tennessee, on the Mississippi River. Fort Wright was Tennessee's first military training camp in the Civil War and is named after Marcus Joseph Wright. Later in the war Wright was the Confederate military governor of Columbus, Kentucky, from February 1862 until its evacuation, and with his regiment was present at Belmont and Shiloh. After serving on the staff of Maj. Gen. Benjamin F. Cheatham, he was promoted to brigadier general on December 13, 1862, and fought at Chickamauga and Missionary Ridge. In 1863-64 he was in charge of the district of Atlanta. After the evacuation of the city he commanded at Macon, and then in Mississippi and western Tennessee.
After the war Wright became the editor of the Columbia, Tennessee, Journal and later moved to Washington, D.C., to become a lawyer.
After 1878 Wright was agent of the United States War Department for collecting Confederate military records. He published numerous works, including:
- Life of Gov. William Blount (1884)
- Life of General Scott (1894)
- Analytical Reference (1904)
- Tennessee in the War (1908)
- General Officers of the Confederate Army (1911)
- The Social Evolution of Woman (1912)
Wright died in Washington, D.C., and is buried in Arlington National Cemetery, one of only two former Confederate officers there (the other being Joseph Wheeler).
- "Diary of Brigadier-General Marcus J. Wright, C.S.A.". Documenting the American South. University of North Carolina at Chapel Hill. 1989. http://docsouth.unc.edu/fpn/wrightmarcus/wright.html. Retrieved 2009-03-29.
- "TN Encyclopedia: Tipton County". The Tennessee Encyclopedia of History and Culture. http://tennesseeencyclopedia.net/imagegallery.php?EntryID=T097. Retrieved 2008-10-04.
- Eicher, John H., and Eicher, David J., Civil War High Commands, Stanford University Press, 2001, ISBN 0-8047-3641-3.
- Arlington National Cemetery biography of Wright