Father Coyne, a native of Baltimore, Maryland, had been director of the observatory since 1978.
The Vatican press office announced the new director on Saturday.
Father Funes, 43, is a native of Cordoba, Argentina. He earned a degree in astronomy from the University of Cordoba.
He studied theology in Rome at the Gregorian University, and earned a doctorate in astronomy from the University of Padua in 2000. Father Funes has done considerable research on disk galaxies.
Pope Gregory XIII established the Vatican Astronomical Observatory to study the elements necessary to reform the liturgical calendar, which took place in 1582.
After a long period of inactivity, Pope Leo XIII founded the new Vatican Astronomical Observatory in 1891. The main headquarters of the Vatican Observatory is in Castel Gandolfo.
In 1981, when the Roman skies became too luminous for observation, the Vatican Observatory Research Group was founded in Mount Graham, Arizona.