He graduated from Harvard University in 1797. Studied law; was admitted to the bar and commenced practice in Groton, Massachusetts, in 1804.
He was elected as a Democratic-Republican to the Twelfth Congress to fill the vacancy caused by the resignation of Joseph B. Varnum. And was reelected to the Thirteenth Congress and served from November 4, 1811, to April 18, 1814, when he resigned. Richardson moved to Portsmouth, New Hampshire, in 1814.
He became a United States Attorney in 1814.
And in 1816 was appointed chief justice of New Hampshire and served as chief justice until his death in 1838 in Chester, New Hampshire, where he is buried in the Old Cemetery. He was the uncle of William Adams Richardson who was United States Secretary of the Treasury from 1873 to 1874.
Dartmouth College gave him the degree of Doctor of Laws He was elected a member of the American Antiquarian Society in 1819.