Born in Hyannis, Massachusetts in 1849, Elijah Baxter moved to Rhode Island as a young man. Before he was twenty, his artistic talents were widely recognized by fellow Providence artists. Around 1867, a large group of artists, including Edward M. Bannister and Edward C. Leavitt, were greatly impressed by the young man’s abilities and held a benefit sale, using the proceeds to provide Baxter with a studio to launch his career.
In 1873, after studying abroad, Baxter returned to Rhode Island and established studios, first in Providence, then Warwick, and eventually in Newport on the Clews Estate at the west end of Bailey’s Beach. It was in Newport that he produced most of the seascapes for which he became best known. Baxter was a charter member of the Newport Art Association and was instrumental in the founding of the Rhode Island School of Design. He was also a member of the Providence Art Club, the Boston Art Club and the St. Boltoph Club at Boston.