Born in New York, he attended Princeton, taught for a short period therafter, and subsequently earned a law degree and set up a law practice.
He soon joined the Democratic-Republican Party and served in the state legislature briefly prior to being appointed to the state Supreme Court, on which he served for sixteen years (including four as chief justice).
However, his primary ambition was for political office. He was appointed Secretary of the Navy under President James Monroe, and campaigned for the Democratic-Republican Presidential nomination for the 1824 race. When Andrew Jackson won the nomination, Thompson only reluctantly accepted accepted Monroe's nomination to the Court. He did not gave up his ambitions for politics there, and took the unusual step of running for political office from the bench; however, his 1828 bid for Governor of New York was unsuccessful. Thereafter he mostly exited political life, and on the court was a staunch opponent of Chief Justice John Marshall.