Brown studied with a private tutor, and was proficient in French, Latin and Greek. He studied law under Alexander Hamilton for five years, and was admitted to the bar in 1802.
He served as the seventh Governor of Ohio. He moved near Cincinnati, Ohio in 1803. He was appointed to the Ohio Supreme Court in 1810 and was re-elected in 1817.
Brown was elected to the governorship a year later and was re-elected in 1820.
He resigned on January 3, 1822 to take office in the United States. Senate after the death of William A. Trimble. He was defeated for re-election in 1824 by William Henry Harrison.
Brown was the Ohio Presidential elector in 1828 for Andrew Jackson. An active supporter of Andrew Jackson, Brown was appointed Chargé d"Affaires to Brazil in 1830 and served for four years.
He then served as commissioner of the General Land Office in Washington, District of Columbia from 1835 to 1836.
In 1836, he retired to a family farm in Indiana most likely staying at the David Brown House in Ohio County. Brown later served a single term in the Indiana House of Representatives from 1841 to 1843. Brown died in Indianapolis, Indiana at a Democratic Convention, and is buried in the Cedar Hedge Cemetery located in Rising Sun the county seat of Ohio County, Indiana.
Elected a member of the American Antiquarian Society in 1818.