He entered the Society of Jesus in Rome on 30 Oct., 1836, and studied at the Roman College where he followed the courses of Father Vincent Caraffa, the professor of mathematics; he was appointed assistant to Father De Vico, director of the Vatican Observatory. He was ordained in 1844, and filled the chair of higher mathematics at the Roman College, when the Revolution of 1848 caused his precipitate flight from Rome; coming to America he lived at Georgetown College, except for a few years, until 1869. He was stationed at Woodstock, Maryland, at the opening of the scholasticate, and remained there until 1884. He founded the American Messenger of the Sacred Heart in 1866, and retained editorial control of it until 1885; during these years he was also head director of the Apostleship of Prayer in the United States. He had many difficulties to contend with in launching and sustaining the "Messenger", and in directing the League of the Sacred Heart. He was also the architect of St. Aloysius Church, Washington, DC. On account of failing health, he was transferred in 1885 to the novitiate, Frederick, Maryland, where paralysis terminated his career. It was said of him that he had two passions---one for pure mathematics, and the other for the Catholic religion.
In astronomy, his work includes Catalogue of Star-Colors, published in his Memoirs of the Roman College, 1845 and 1847. The second memoir includes the first, and forms the entire catalogue, except the twelve celestial charts that accompanied the first. The Revolution broke out in Rome when the second memoir was in the printer's hands, and prevented the completion of the work. The colour catalogue is the first general review of the heavens for star-colours, from the North Pole to 30 degrees south of the Equator.
At Georgetown Observatory, in 1850, Sestini made a series of sunspot drawings, which were engraved and published (44 plates) as "Appendix A" of the Naval Observatory volume for 1847, printed in 1853. His last scientific work as an astronomer was the observation of the total eclipse of July 29, 1878, in Denver, Colorado. A sketch of the corona as it appeared to him was published in the Catholic Quarterly Review. From his arrival at Georgetown (1848) until his retirement from Woodstock (1884) he had been almost constantly engaged in teaching mathematics to the Jesuit scholastics, and he published a series of textbooks on algebra, geometry and trigonometry, analytical geometry, and calculus. He wrote treatises on natural science for the use of his pupils; some of these were lithographed and others were privately printed at Woodstock: Theoretical Mechanics in 1873; Animal Physics in 1874; Principles of Cosmography in 1878.