Richardson was born to Willis Baker Richardson and the former Nannie Coon on Sandy Creek near the community of Caddo in Stephens County, Texas, which had a population in the 1890 census of only seventy-five persons. He attended Simmons College (later Hardin-Simmons University), from which he procured his Bachelor of Arts degree in 1912. He then moved to Chicago, Illinois, where he received a Bachelor of Science in 1914 from the University of Chicago. In 1915, Richardson wed the former Pauline Mayes (April 17, 1892–April-1965); the couple had one son, Rupert Richardson, Jr.

From 1915-1916, Richardson was principal of Cisco High School in Cisco, a town in Eastland County east of Abilene. The next academic year, he was principal at Sweetwater High School in Sweetwater, the seat of Nolan County, located west of Abilene. In 1917, he returned to his alma mater, Simmons College, as professor of history. He served briefly as a second lieutenant in the United States Army during World War I. He subsequently procured his Master of Arts in 1922 and his Ph.D. in 1928, both from the University of Texas at Austin, where he studied under Eugene C. Barker. He was dean of students at Hardin-Simmons from 1926—1928, vice president from 1928—1943, acting president from 1943—1945, and president from 1945-1953. Under his presidency the institution expanded in enrollment and size of the physical campus. In 1953, he retired as the Hardin-Simmons president emeritus and returned to the history department, where he continued to teach courses and supervise student theses.

Richardson’s scholarly works include The Comanche Barrier to South Plains Settlement (1933), a study of the Comanche Indians; The Greater Southwest (1934), coauthored with Carl Coke Rister, Adventuring with a Purpose (1952); The Frontier of Northwest Texas (1963); Colonel Edward M. House: The Texas Years (1964), a study of Woodrow Wilson’s political aide from Houston, and Caddo, Texas: The Biography of a Community (1966). His personal reflection is unveiled in Famous Are Thy Halls: Hardin-Simmons University As I Have Known It (1964).

His history textbook, Texas: The Lone Star State (1943) went through five editions until it ceased to be the leading textbook in its field during the 1980s. Texas: The Lone Star State, now in its tenth edition and co-authored by Ernest Wallace, Adrian Anderson, and Cary D. Wintz, emphasizes the 19th century and treats Reconstruction as a political tragedy or melodrama, the earlier view usually held by southern historian but subsequently abandoned after the rise of the civil rights movement. Richardson served as an editor of the West Texas Historical Association Year Book from its first issue in 1925 until his death. At the time the association was based at Hardin-Simmons, but it relocated in 1998 to Texas Tech University in Lubbock.

A fellow of the Texas State Historical Association, Richardson also served from 1969-1970 as president of the organization. He was a former president of the Southwestern Social Science Association, the Texas Philosophical Society, and the Texas Council of Church-Related Colleges and Universities. He was also active in the Masonic lodge, the Lions Club, and in Baptist affairs.

Richardson was a member from 1953-1967 of the Texas State Historical Survey Committee, now the Texas Historical Commission, and promoted the expansion of historical markers along Texas highways. In 1972, he received the Ruth Lester Lifetime Achievement Award for his work in historical preservation.

In 1965, shortly after the death of his wife, Richardson traveled to Washington, D.C., to testify on behalf of the establishment of the Guadalupe Mountains National Park in West Texas near the New Mexico state line. The park opened in 1967.

Richardson died in Abilene two weeks prior to what would have been his 97th birthday. He is permanently honored by the naming of both the Richardson Library and the Richardson Research Center of the Southwest on his campus. In addition, the West Texas Historical Association names its annual book award in Richardson's honor.B W Aston, Hardin-Simmons history faculty member, headed the research center from 1981-2001.