He entered the Society of Jesus in Rome on October 30, 1836, and studied at the Roman College (now Pontifical Gregorian University) where he followed the courses of Vincent Caraffa, the professor of mathematics.

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.

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; and Principles of Cosmography in 1878.

Sestini 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.

Because his health was declining, he was transferred in 1885 to the novitiate in Frederick, Maryland, where paralysis eventually ended his career.