He was educated at the College of William and Mary.
After College he studied law, was admitted to the bar, and began practice in Richmond. He was a member of the House of Delegates from 1809 to 1821, excepting the year 1817. He was speaker of this body from 1812 until 1815. In 1814 and again in 1816 he ran for Congress but was defeated. The next year he became a director of the Richmond branch of the Bank of the United States.
He finally was successful in his campaign for Congress and served from 1821 to 1834, when he resigned. During this period his political influence became important on the federal theatre. Being an early supporter of Van Buren, he went over into the Jackson camp with his chief and became a member of the "Richmond Junto, " which, beside himself, consisted of Spencer Roane, Thomas Ritchie, and William C. Rives.
In 1827, with the support of Van Buren, he was elected speaker of the federal House of Representatives and served until 1834. Adams accused him of double dealing on the tariff question, and he immediately won the hatred of the opposition by appointing committees on a strictly partisan basis, thus breaking with the policy established by his immediate predecessors in office. When the nullification controversy arose, he took the side of the Union and was one of the few congressmen of that persuasion who weathered the storm in Eastern Virginia. His stand was an important factor in preventing Virginia from following the lead of South Carolina in this matter.
In 1832 he supported Van Buren for the vice-presidency and in 1835 was chairman of the Baltimore convention that nominated Van Buren for the presidency.
In 1834 Stevenson was nominated by President Jackson as minister to Great Britain. The Senate refused to confirm his nomination at the time, but Jackson made no other appointment, and finally in 1836 Stevenson's appointment was confirmed. While serving in this capacity, he brought embarrassment upon himself by advising certain British investors that he believed the attack upon the Bank of the United States would fail. His service in England was terminated in 1841 by the Whig triumph of the previous year.
Returning to Virginia, he made his home at "Blenheim" in Albemarle County, an estate that he had purchased in 1836. Ritchie tried to obtain his return to active political life when Polk was elected to the presidency, but the Polk administration did not accept the suggestion.
He died at "Blenheim" in 1857.
He was married three times: first, to Mary Page White, the daughter of John White and the grand-daughter of Carter Braxton, second, in 1816, to Sarah Coles, and third, to Mary Schaff, of Georgetown. His son was John White Stevenson.