The pair asked the priests for up to 10,000 euros each to keep quiet about their virtual sex sessions via webcam and in some cases, actual encounters, Panorama said.
The weekly cited a judicial probe spearheaded by magistrates in the town of Isernia in Italy's southern Molise region, which led to the arrest on 26 July of 35-year-old Diego Maria Caoggiano and Giuseppe Trementino, aged 30.
The men live together in the town of Bagnoli del Trigno, where they have been granted house arrest, Panorama said.
Police found the contact details of over 100 priests on computers and mobile phones belonging to the suspects, as well as video recordings of sex sessions involving priests and incriminating messages in what prosecutors described as a "disturbing" case.
Trementino, a despatch rider, told Panorama through his lawyer that he had initially been seduced by a priest who he had delivered a parcel to and had sex with soon after they exchanged phone numbers. The priest had made regular payments to him via Postpay "often of his own free will" and had offered to buy him a car, Tremonti claimed.
The priest reported Trementino to police in May but he meanwhile met another priest on the social networking website Facebook. Trementino claimed to have spent three days with the priest in a hotel in Rome during a conference, and said the priest paid for his rail ticket and gave him 300 euros "to buy canabis, alcohol, condoms and lubricants".
Trementino claimed he was soon inundated with erotic messages and requests for sex from "dozens" of priests with whom he came into contact on Facebook and Messenger.
"I would begin to speak to them using dirty talk and they would get undressed and masturbate," he said. "I would get up to five requests a day, and even had one from France" he said.
"Asking them for money was a way of filtering the requests, which had got out of hand, he said, adding that he became "disgusted" by the priests' "absurd" and "asphixiating" needs.
Caggiano, who had access to Trementino's computer and to his friends' social networking profiles, appears to have been the chief blackmailer, asking some priests for up to 10,000 euros, according to investigators.
One priest who paid out 7,000 euros to the pair said he had to use money given to him by parishioners for blessing their homes.
There are "a multitude of priests" in Italy who are keen for sexual contact via the Internet, where they exchange information on the casual partners they meet there, Isernia prosecutors said, cited by Panorama.