Luke Wright was born on August 29, 1846, in Giles County, Tennessee. He enlisted in the Confederate Army, becoming second lieutenant, and was cited for bravery under fire during the 1863 Battle of Murfreesboro, Tennessee. After the war, Wright spent time at the University of Mississippi, studied law, worked in his father's law office in Memphis, and then served as district attorney general of the city from 1870 to 1878.

Wright also took over as interim mayor of Memphis during a yellow fever epidemic. He was appointed vice governor of the Philippines, serving between 1901 and 1904, and then from 1904 to 1905 as governor general. President Theodore Roosevelt named Wright secretary of war following the resignation of William Howard Taft, and he served until the end of the Roosevelt administration. President Taft's refusal to retain Wright in that post contributed to a growing rift between Taft and TR. Wright died at his home in Memphis on November 17, 1922.