Born in New Castle, Kentucky, Thomasson completed preparatory studies. He served in Captain Duncan's company in the War of 1812. He studied law. He was admitted to the bar and commenced practice in Corydon, Indiana, before he was twenty-one years of age. He served as member of the State house of representatives in 1818–1820. He served as prosecuting attorney of Corydon in 1818. He moved to Louisville, Kentucky, in 1841.
Thomasson was elected as a Whig to the Twenty-eighth and Twenty-ninth Congresses (March 4, 1843 – March 3, 1847). He declined to be a candidate for renomination. He moved to Chicago, Illinois, and resumed the practice of law. During the Civil War served in the Union Army in the Seventy-first Regiment, New York Volunteer Infantry. He died near La Grange, Kentucky, December 29, 1882. He was interred in Cave Hill Cemetery, Louisville, Kentucky.