He was born in Amesbury, Massachusetts, fourth son of Stephen Bartlett. In 1745 he began the study of medicine under a Dr. Ordway of Amesbury. In the 1750s he opened a practice in Kingston, New Hampshire.

Bartlett eventually became interested in politics, and in 1765 was elected to the colonial assembly, where he began to oppose the policies of the royal governor, John Wentworth. As a gesture of good will, Wentworth appointed Bartlett as a justice of the peace. Nevertheless, in 1774 the colony's assembly (meeting illegally, having been recently dissolved), appointed Bartlett and John Pickering as delegates to the Continental Congress, although Bartlett had to decline because his house had burned down. Bartlett was elected to Congress again in the following year, and attended thereafter.

When the question of declaring independence from Great Britain was officially brought up in 1776, as a representative of the northernmost colony Bartlett was the first to be asked, and answered in the affirmative.

He was re-elected to Congress in 1778, but partway through the session he returned to New Hampshire to attend to personal business. Thereafter, he remained in the state, becoming a justice of the state supreme court in 1782 and chief justice in 1788. He was an advocate in the state for adoption of the Constitution in the following year, and was elected to be a U. S. Senator, but declined the office. Starting in 1791 Bartlett served as chief executive of New Hampshire (initially with the title of the president, then as governor after the title was changed in 1792). After resigning the governorhip in January 1794 because of declining health, he died the next year.

The Josiah Bartlett elementary school is a visible presence on the only direct four-season route through the town of Bartlett, New Hampshire.