Thompson came to America with his widowed mother in 1847 and settled in Albany, New York. He worked in the office of a professor of anatomy and studied at the local medical college where he became known for his abilities at dissection. As he studied for a medical career, he drew as a hobby but soon gave up the former in favor of the latter. He was accepted as a student of Albany sculptor Erastus Dow Palmer in about 1849 and became his assistant in 1854. During those years, he executed a small bust for his friend the artist Frederick S. Church and a relief of Dickens' Little Nell. His first portrait bust was of Dr. James H. Armsby in whose office he had worked before meeting Palmer. In 1858, he went to New York and established his own studio in the famous Tenth Street Studio building which had only recently opened.
Evidently Thompson was an apt student in Palmer's studio and had learned from the master the correct execution of cameos and portrait reliefs. In 1859, not long after his arrival in New York, he exhibited a number of cameos at the National Academy (cat. no. 32). The following two years he exhibited marble medallion portraits and a portrait bust of an unnamed subject. He continued to exhibit at the Academy throughout the 1860s, 1870s, and into the 1880s. His work in portraiture was obviously impressive enough that he was elected an associate of the Academy after he had been in New York for barely a year. He was a member of the life class in the Academy school in 1859 and 1860.
Among those works by Thompson which were best known during his own lifetime were Morning Glory, a profile portrait of a young girl, The Trapper, which he showed at the Academy in 1862 (cat. no. 82), a relief portrait of Candace Wheeler (1863; New York Historical Society), and a bust of William Cullen Bryant (1865; a version is in the Metropolitan Museum of Art), which became the definitive portrait of the author.
In 1865, Thompson was working on his first large sculpture, a statue of Napolean, which was completed and exhibited at the 1867 Paris Exposition to favorable reviews. The sculptor went himself to Europe that same year and lived and worked among the expatriate colony in Rome. Not having received any major commissions, however, he was forced to return to America in 1869.
During the 1870s he executed a number of portrait busts of his fellow artists including Charles Loring Elliot (1870; Metropolitan Museum), Sanford R. Gifford (1871; Metropolitan Museum), and Samuel F. B. Morse (see below). In 1869, he was asked by the Academy's Council to model a bust of the late James A. Suydam in relief for use on a medal which was struck to commemorate Suydam. (The immediate result of the commission, a small plaster mounted on wood and dated 1870 which was at one time in the Academy's collection, is now missing. A similar relief portrait of Charles Loring Elliott modeled by Thompson and presented by him to the Academy at the same time he presented the Suydam portrait has likewise disappeared).
During the decade of the 1870s, the longed-for major commissions finally began coming to Thompson. He produced major statues of General Winfield Scott and Admiral Samuel du Pont (now in Wilmington, Delaware) for the city of Washington, D. C., and one of Abraham Pierson for Yale Collegiate School.
Thompson returned to Europe in 1875, this time settling in Florence where he remained for six years. His period of productivity was over, however, and by the time he returned to New York in the early 1880s, he was suffering from psychological difficulties that eventually caused him to be committed to a hospital in 1892.
After his death, the Council of the Academy recorded the following statement concerning him: "During his active career Mr. Thompson was among the most brilliant sculptors of this country, and his works in the Century Club, the [Metropolitan] Museum of Art, and other public places, are so fine, that it is a source of pride that he was a member of this Institution."