Ambrose Hundley Sevier was born near Greeneville, Tennessee in Greene County, Tennessee. Sevier moved to Missouri in 1820 and to Little Rock, Arkansas in 1821.
In Arkansas he became clerk of the Territorial House of Representatives. He studied law and was admitted to the bar in 1823. Sevier became a member of the House of Representatives and served from 1823 to 1827 and served as speaker of that body in 1827.
Sevier was elected as a Delegate to the Twentieth US Congress to fill the vacancy caused by the death of Henry Wharton Conway. Sevier was reelected and served as delegate in three successive congresses from 1828 to 1836 when Arkansas was admitted to the Union. Sevier is known as the "Father of Arkansas Statehood".
In 1836 Sevier was elected as the first member of the United States Senate from Arkansas. He was reelected in 1837 and 1843. He resigned from office in 1848. During the twenty-ninth Congress he was allowed to hold the seat of President pro tem of the Senate for a day, though he was not actually elected to that post. During his tenure he served as chairman of the Committee on Indian Affairs and was a member of the Committee on Foreign Relations.
In 1848 Sevier and Nathan Clifford, the Attorney General of the United States, were appointed ambassadors to Mexico by President James K. Polk to negotiate the Treaty of Guadalupe Hidalgo at the end of the Mexican-American War.
Ambrose Hundley Sevier died on his plantation in Pulaski County, Arkansas. He was buried in the historic Mount Holly Cemetery. The State of Arkansas erected a monument in the cemetery in his honor.
Sevier was the grandnephew of John Sevier, first cousin of Representative Henry Wharton Conway, Governor James Sevier Conway, Governor Elias Nelson Conway, brother-in-law of Senator Robert Ward Johnson and father-in-law of Governor Thomas James Churchill.
Sevier County, Arkansas is named in his honor.