He graduated from Harvard University in 1782, studied law, was admitted to the bar in 1786 and commenced practice in Mendon, Massachusetts.
He was town treasurer in 1794 and 1795, and was elected one of the first school commissioners in 1796. Hastings was elected as a Federalist to the Seventh Congress to fill the vacancy caused by the resignation of Levi Lincoln. He was reelected to the Eighth and Ninth Congresses and served from August 24, 1801 to March 3, 1807.
From 1819 to 1828, he was chief justice of the court of sessions for Worcester County.
Hastings died in Mendon. Interment was in the Old Cemetery.
William Soden Hastings, Seth Hastings" son, also represented Massachusetts in the House of Representatives.
He declined to be a candidate for renomination in 1806 and was a member of the Massachusetts State Senate in 1810 and 1814.
Children include William Soden.