Born in Scotland, he immigrated to North Carolina in 1772 with his parents. He graduated from the College of New Jersey (now Princeton University) in 1794 and began studying law. He was admitted to the bar in North Carolina and began practicing in Knoxville, Tennessee.
He was elected to the United States House of Representatives as the Representative from Tennessee's at-large congressional district in 1803. He served in the House from 1805-1809, in the 8th, 9th, and 10th Congresses). During the 10th Congress, he was the chairman of the Ways and Means Committee. He was also one of the managers appointed in 1804 to conduct the impeachment hearings for John Pickering, judge of the United States District Court for the District of New Hampshire, and later in the same year, the impeachment hearings against Samuel Chase, Associate Justice of the Supreme Court of the United States.
He left Congress in 1809 to become judge of the Tennessee Supreme Court, serving until 1811.
He served as a United States Senator from Tennessee twice, once from 1811 to 1814, having been elected to fill the seat of Jenkin Whiteside, and again from 1815 to 1818. His first service was from October 8, 1811 to February 11, 1814, when he resigned to accept appointment as the United States Secretary of the Treasury. He returned to the Senate on October 10, 1815. He served as the first chairman of the Senate Finance Committee and its predecessor from December 4, 1815, until his resignation from the Senate on April 20, 1818; on this occasion to accept appointment as United States Ambassador to Russia, a position he held from 1818-1821. Campbell served as a member of the French Spoliation Claims Commission in 1831.
Appointed Secretary of the Treasury by James Madison, he faced national financial disorder brought on by the War of 1812. Congress had failed to recharter the First Bank of the United States after its charter expired in 1811, and appropriations for the war were unavailable, so Campbell had to convince Americans to buy government bonds. He was forced to meet to lenders terms, selling government bonds at exorbitant interest rates. In September, 1814 the British occupied Washington, D.C. and the credit of the government was lowered even further. Campbell was unsuccessful in his efforts to raise money through additional bond sales and he resigned that October after only eight months in office, disillusioned and in bad health.
Campbell County, Tennessee, is named in his honor.