Greg Burke, an American, and Paloma García Ovejero, who is Spanish, have resigned with effect from tomorrow as the Vatican press office director and his deputy in charge of Vatican communications with the media.
Burke announced the news on Twitter, writing, "at this time of transition in Vatican communications, we think it's best the Holy Father is completely free to assemble a new team".
Tornielli has worked as a Vatican correspondent for several Italian newspapers and publications for over 20 years, according to Vatican News.
Pope Francis moved quickly after his election in 2013 to make overtures to Jews and Muslims, inviting two old friends from Buenos Aires - a rabbi and a Muslim professor - on a trip to the Middle East where he condemned religious hatred. Among those named are prominent Italian Vatican experts Roberto de Mattei, Sandro Magister and Antonio Socci.
The Pontiff was presented with the ball by a member of the Circus of Cuba during his weekly general audience in the Pope Paul VI hall, at the Vatican.
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Vigano released part of a letter by former Pope Benedict that was to have remained private, using it to promote a book on the theology of Pope Francis. In August, Tornielli published a report of alleged "facts and omissions" from Viganò's testimony, unsuccessfully attempting to discredit the whistleblower.
The pope has named Alessandro Gisotti as interim head of the Vatican press office, it said.
"Faced with what is their autonomous and free choice, I can only respect the decision they have made", he said, "their significant commitment has contributed to the [Catholic Church's] path of reform".
During a speech past year in Peru, Francis apologized for asking for evidence of abuse from victims while again casting doubt on their claims.
The resignations clearly took the new team by surprise. Dario Edoardo Viganò from his position as head of the Vatican Secretariat of Communications earlier this year.