The Portrait of Maffeo Barberini features Pope Urban VIII, who hailed from the noble Barberini family and was a friend of Caravaggio's patron.
Born in 1568, wealthy humanist Barberini was elected in 1623 to Saint Peter's throne, which he held until his death in 1644.
The painting was authenticated in 1963 by art critic Roberto Longhi, an expert in the work of the 16th-century artist.
Longhi said the undocumented painting was part of the Barberini family collection for centuries before passing into private hands in the 1930s.
Caravaggio - The Portrait Unveiled will run from November 23rd to February 23rd at the Barberini Palace, which now houses part of the National Galleries of Ancient Art.
The Palace also permanently houses four other works by Caravaggio: Judith Beheading Holofernes, Narcissus, Saint John the Baptist and Saint Francis in Meditation.
Maffeo Barberini was "not only an extremely powerful man of power, but also a great and refined intellectual," gallery director Thomas Clement Salomon told AFP.
Caravaggio's portrait of him is "of very great value," he said
"It has never been lent to an exhibition, it has never been seen in a museum, so it is an absolute preview," he said.
"The portraits painted by Caravaggio can be counted on the fingers of one hand, so being able to show one to the public and to experts is exceptional."
The Maffeo Barberini portrait, with its sparsely coloured decor, "plays on light and shadow", Caravaggio's signature style, art historian and curator Paola Nicita told AFP.
"The heart of the painting lies in the hands: the left hand clutching a letter...and the right hand emerging from the painting, entering our space," she said.
"It is a painting that expresses itself through gestures," she added.
"This marvellous gesture of the outstretched right hand is very reminiscent of the gesture of Christ in The Calling of Saint Matthew," she said, referring to one of Caravaggio's most famous works, which is displayed in the Church of St Louis of the French in Rome.
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