Wright was admitted to the Luzerne County, Pennsylvania bar on April 7, 1820. When he was twenty-four, he moved to the Pensacola area. He became friends with and went to work for Richard K. Call, a protégé of Andrew Jackson. In April of 1824 he was appointed to the territorial council. In May, the president appointed him United States Attorney for Middle Florida, and then for West Florida in February of 1826.
His political career encountered difficulties after he accused Judge Henry Marie Brackenridge of malfeasance in November 1827. The judge retaliated by seeking Wright's replacement through a letter writing campaign and his political connections. As a result, another man was appointed in his place when his term expired in 1830. He represented Escambia County in the territorial council from 1831 to 1833 and again in 1837. He served as a member of the 1838 constitutional convention till January 5, 1839. That year, he became a member of the Territorial Senate.
He left office to work behind the scenes politically. He served in the Florida Senate in 1845, and again returned to his law practice. In 1850 he became an Alabama and Florida Railroad commissioner. The governor appointed him to the Supreme Court in 1853 to replace Walker Anderson. He was replaced in turn when the voters elected Thomas Baltzell, the first Florida Justice chosen by popular election.
He again returned to his Pensacola business interests and law practice. He became president of the Alabama and Florida Railroad in 1856. He served on the 1865 constitutional convention, but never again served as an elected official. He died on April 28, 1874.