Ogden was born in Elizabeth, New Jersey (formerly Elizabethtown). He graduated from the College of New Jersey (now Princeton University) in 1773, and served as tutor in Barber’s Grammar School from 1773-1775. In the American Revolutionary War, Ogden served as a lieutenant, captain, and brigade major. After studying law, Ogden was admitted to the bar in 1784 and commenced practice in Elizabeth.

Ogden served as a presidential elector in the 1796 electoral college that elected John Adams. He was clerk of Essex County from 1785-1803, and was elected as a Federalist to the United States Senate to fill the vacancy caused by the resignation of James Schureman and served from February 28, 1801, to March 3, 1803. He lost his bid for reelection to the Senate in 1802. In 1803, Ogden was elected to the New Jersey General Assembly, where he served until 1812. Ogden was elected trustee of the College of New Jersey (later to become Princeton University) in 1803, a post in which he served until his death. Ogden was elected as Governor of New Jersey in 1812.

Ogden was nominated by President James Madison as major general of the Army in 1813, but declined the appointment. He became engaged in steamboat navigation in 1813, and was defendant in the historic Gibbons v. Ogden case that denied New York State's attempted monopoly on steamboat operation between New York and New Jersey. Ogden moved to Jersey City in 1829 and resumed the practice of law. In 1830, he was appointed as collector of customs and served until his death in Jersey City. Ogden's body is interned at the First Presbyterian Church Burial Ground in Elizabeth.

Ogden's nephew Daniel Haines later also served as Governor of New Jersey.