Jackson was the youngest son of Joseph and Susannah (Gray) Jackson. Before the American Revolutionary War, he was an officer of the First Corps of Cadets in Boston, which was disbanded during the British occupation. After the evacuation, six former cadet officers organized a company of seventy-eight officers and men called the Boston Independent Company on 17 March 1776, with Jackson as their commander. In January 1777, the unit was taken into Continental service, designated Jackson's Additional Continental Regiment. He led his regiment in the Philadelphia campaign of 1777, at Monmouth and Rhode Island in 1778, and at Springfield, New Jersey in 1780. In 1780 the regiment was taken into the Massachusetts Line and renamed the 16th Massachusetts Regiment.