It was named after Claremont, the country mansion of Thomas Pelham-Holles, Earl of Clare. On October 26, 1764, Colonial Governor Benning Wentworth granted the township to Josiah Willard, Samuel Ashley and 67 others. Although first settled in 1762 by Moses Spafford and David Lynde, many of the proprietors arrived in 1767, with a large number from Farmington, Hebron and Colchester, Connecticut. The undulating surface of rich, gravelly loam made agriculture an early occupation.
It was water power from the Sugar River, however, which brought the town prosperity during the Industrial Revolution. Large brick factories were built along the stream, including the Sunapee Mills, Monadnock Mills, Claremont Machine Works, Home Mills, Sanford & Rossiter, and Claremont Manufacturing Company. Principal products were cotton and woolen textiles, lathes and planers, as well as paper. Although like other New England mill towns, much industry moved away or closed in the 20th-century, the city's former prosperity is evident in some fine Victorian architecture, including the 1897 city hall and opera house.
In 1874, businesses in Claremont included Monadnock Mills, manufacturing cotton cloths from one to three yards wide, Marseilles quilts, union flannels, and lumber and employing 125 males and 225 females; Home Mill (A. Briggs & Co.) producing cotton cloth and employing 8 males and 20 females; Sullivan Machine Co., manufacturing Steam Dimond Drill Machinery for quarrying rock, turbine water wheels, cloth measuring machines, and doing general machine and mill work, employing 56 males; Sugar River Paper Mill Co., manufacturing printing paper and employing 30 males and 20 females; Claremont Manufacturing Co., manufacturing paper and books, and doing stereotyping and book and job printing, employing 34 males and 34 females; Russell Jarvis, manufacturing hanging paper and employing 7 males and 2 females; John S. Farrington, manufacturing straw wrapping paper and employing 5 males and 1 female; Sullivan Mills, (George L. Balcom) manufacturing black doeskins and employing 20 males and 18 females; Charles H. Eastman, in the leather business and employing 4 males; Sugar River Mill Co., manufacturing flour, feed, and doing custom grinding, and employing 8 males; three saw mills employing a part of the year, 10 males; Blood & Woodcock, in the business of monuments and grave stones and employing 8 males; and Houghton, Bucknam & Co., in the business of sashes, doors and blinds, employing 8 males.
In March 1989, the Claremont School Board voted to initiate a lawsuit against the State of New Hampshire, claiming that the state's primary reliance upon local property taxes for funding education resulted in inequitable educational opportunities among children around the state and a violation of their constitutional rights. Following a lawsuit and a series of landmark decisions, the New Hampshire Supreme Court agreed. Known as "The Claremont Decision", the suit continues to drive the statewide debate on equitable funding for education; and Claremont continues to play a primary role in this legal challenge.
The city of Claremont, California, was named for Claremont, New Hampshire.