Culberson was born in Troup County, Georgia, on September 29, 1830, the son of David B. and Lucy (Wilkerson) Culberson. After leaving Brownwood Institute in La Grange, Georgia, he read law at Tuskegee, Alabama, in the school of William P. Chilton, Chief Justice of Alabama. He was admitted to the bar in 1850 and began practice in Dadeville, Alabama. In 1856, he moved to Texas and settled in Upshur County, where he practiced law in partnership with Gen. Hinche P. Mabry until 1861, when he moved to nearby Jefferson, Texas. On December 8, 1852, he married Eugenia Kimball; they had two sons, one of whom, Charles A. Culberson, became Governor of Texas and later U.S. Senator. Culberson was a Mason and an Odd Fellow.
Culberson was a member of the Texas Legislature from Upshur County during the 1859-60 session. Because Culberson opposed secession and his district favored it, he resigned his legislative seat. Despite his views on secession, when Texas did secede, Culberson raised the 18th Texas Infantry, and he became its commander with the rank of lieutenant colonel. The 18th Infantry saw combat at Vicksburg in 1862-63, but Culberson's health deteriorated and he was assigned to Austin as Texas Adjutant General. In 1864, he was elected to the legislature from Cass, Titus, and Bowie counties and resigned his military position to rejoin the legislature.
As a prominent Jefferson lawyer he was one of the defense attorneys in the Stockade Case of 1869, and he helped defend accused murderer Abe Rothschild in the Diamond Bessie murder trial. He worked to obtain the acquittal for treason of the then 16-year-old William Jesse McDonald, then of Rusk County, the later Texas Ranger. Culberson attended the Democratic state convention in 1868 and served as a presidential elector in the Presidential Election of 1872 pledged to Horace Greeley (who died before Texas' electoral votes could be cast) but casting his ballot ultimately for Benjamin Gratz Brown. Culberson was elected to the State Senate in 1873 representing Marion, Cass and Bowie Counties. In 1874, he ran for Congress from the 2nd District of Texas, and won. He resigned his Senate seat to go to Washington.
Culberson served in the United States House of Representatives from 1875–1897, supporting prohibition and opposing federal interference in state government. In 1876, he favored the repeal of the Specie Act, and in 1888 he introduced antitrust legislation in Congress. He represented both the 2nd and later the 4th district and served as Chairman of the Judiciary Committee.
Though in many ways, a populist himself, Culberson campaigned against the Populist Party which was quite strong in Texas in the 1890s. Culberson viewed them as a divisive force in state politics.
He was appointed by President William McKinley on June 21, 1897, as one of the commissioners to codify the laws of the United States and served in this capacity until his death in Jefferson, Texas on May 7, 1900. He was interred in Jefferson.
A distant relation, John Culberson, represents the current Texas 7th Congressional District in the U.S. House.