Putnam was born in Sutton, Massachusetts. He apprenticed as a millwright and taught himself geography and mathematics. During the French and Indian War, he served with a Connecticut regiment in the Great Lakes region. In 1773, he became the surveyor of East Florida after a trip there to assess veterans' land grants along the Mississippi River. In 1775, he joined one of Massachusetts's first Revolutionary regiments. His fortifications protected Dorchester Heights during the British siege of Boston. He supervised the building of defenses around New York City. He refused an appointment as Chief Engineer and took a field command, fighting in the New York campaign that led to the British surrender at Saratoga. He then rebuilt West Point and fought at Stony Point.
After the Revolution, Putnam returned to survey work in Maine (then part of Massachusetts). He supported the award of lands in lieu of back pay to soldiers during the war. Putnam was one of the authors of the army's Newburgh Petition to Congress that requested land disbursements. In 1788, he led a group of Revolutionary veterans to settle Marietta, Ohio, for the Ohio Company. He became a Supreme Court judge for the Northwest Territory. Later, he served in General Anthony Wayne's early campaigns against the Ohio Valley Native American tribes. In 1796, President George Washington appointed Putnam as the first Surveyor General of the U.S. He served in that capacity until 1803. Putnam died on May 4, 1824.