The album, Cantate Domino, includes music written for the Sistine Chapel Choir by Palestrina, Lassus and Victoria during the Renaissance.
It also features two Gregorian chants and a world-premiere recording of the original version of Allegri's Miserere.
The pieces are sung in Latin, as the composers intended.
The chapel is in the Apostolic Palace, the official residence of the Pope, in Vatican City, Rome. The recording took place using a specially-built studio constructed by Deutsche Grammophon, with the mixing desk in an ante-chamber.
Musical dignitaries including Italian opera singer Cecilia Bartoli and Italian choirmaster Roberto Gabbiani attended the recordings.
The chapel is also home to the Papal conclaves, the meetings of the College of Cardinals held when they elect a new Pope.
Grammy-nominated producer Anna Barry described it as an "overwhelming privilege" to record there, among the frescoes of Michelangelo.
The choir has 20 adult singers and 30 boy choristers.
One of the male singers, Mark Spyropoulos, is the first British full-time member of the choir, which is directed by Massimo Palombella.
Palombella said: "After an intensive period of study and scholarship of the sacred music in the Renaissance and its aesthetic pertinence, we have arrived at the point of making the first commercial recording, in this remarkable building.
The Pope will receive the very first copy of the album, which is released on 25 September.
The Pope has given special permission for a studio recording in the Sistine Chapel for the first time, capturing the singing of his own choir.