He graduated from Brown University in 1817, and received a master"s degree in 1820. He also studied law with James Burrill, Junior., and was admitted to the bar in 1820.
In addition to practicing law, Jackson was involved in several businesses, including a cotton manufacturing company. He also built a rubber factory after acquiring patent rights from Charles Goodyear. Jackson"s ventures proved successful, and he later expanded into firearms as operator of the Burnside Rifle Works and a company that manufactured railroad equipment.
In 1843 he was a delegate to the state constitutional convention.
Jackson served as Governor from 1845 to 1846, after defeating incumbent James Fenner. He was elected as a Whig identified with the Liberation movement, which advocated freedom for those imprisoned as a result of the Dorr Rebellion.
Jackson signed a bill freeing rebellion leader Thomas Wilson Dorr and all others who had been convicted. In 1857 Jackson was an unsuccessful candidate for the United States Senate.
Jackson died in Providence on January 21, 1876.
He was buried at North Burial Ground in Providence. Jackson was married twice. He had seven children, five of whom lived to adulthood.
Jackson was active in politics as a Whig, served several terms in the Rhode Island House of Representatives, and was Speaker from 1841 to 1842. In response, Whig opponents of freeing Dorr organized a "Law & Order Party." Jackson was nominated for Governor by the Democrats, and was defeated by Lieutenant Governor Byron Diman.