David Webster Hoyt was born in Amesbury, Massachusetts on April 16, 1833 to Enoch and Elizabeth Williams Hoyt. He attended the Putnam Free School at nearby Newburyport, Massachusetts. Even though Hoyt had resolved that he would never engage in teaching, after graduation he did accept an offer from Dr. Wells, head of Putnam Free School, and taught there from 1851-53. Subsequently he matriculated at Brown University with the class of 1855, but stayed for only for one year. Thereafter he taught at a succession of secondary schools. First he was Principal of the Union School in Beloit, Wisconsin from 1854-55, followed by a position as Principal of Lexington High School in Massachusetts in 1857-58. From 1858-59 Hoyt became an Adjunct Professor in Mathematics and Mechanics of the Polytechnic College of Pennsylvania and then returned to New England with a position in Vermont as Professor of Mathematics and Natural Science at New Hampton Institution, Fairfax, where he taught for the next four years. He received an honorary A.M. from Middlebury Collage in 1861 and in 1864 he became Principal of the English Department of the boys' class of what was then the only high school in Providence, Rhode Island. He continued to teach there as head of the English School when the English and Classical Departments were separated. Hoyt served there for more than 50 years until, in 1914 he retired upon graduating his last class. He was the longest serving pedagogist in the history of the Providence school system and, at his retirement at age 81, was and probably the oldest high school principal in the country. In 1872 he received an honorary A.B. degree from Brown, which further awarded him an A.M in 1909. Moreover he received an honorary Doctor of Science from Rhode Island State College in 1914.

Hoyt was a member of The Providence Franklin Society, whose members presented scientific lectures and undertook scientific excursions around New England. In 1887 he wrote the Franklin Society Report on the Geology of Rhode Island, and in that year served also as President of the Franklin Society. From 1888 to 1893 Hoyt was commissioned to make a topographical survey and a topographical map of Rhode Island. He served as president of the Rhode Island Institute of Instruction from 1880-93. He also published several books related to genealogy, scientific reports, and the history of Rhode Island. Once he remarked that "teaching is my vocation and geology my avocation." That statement was reflected in a long and full life, in which Hoyt managed to combine many interests and accomplishments. On May 8, 1921 he died in his home in Providence, Rhode Island.