He was the son of Col. Robert Harris (1737-1803) of Poplar Tent and Mary Wilson.

His elementary education was at a classical school conducted in association with the Poplar Tent Presbyterian Church, of which his father was a presiding elder.

He then attended the College of New Jersey (now Princeton University) and was awarded the Mathematical Oration at his 1792 graduation.

Harris was a close associate of William Richardson Davie.

He served as the second presiding professor (now known as university president) of the University of North Carolina at Chapel Hill in Chapel Hill, North Carolina, in 1796.