Bertone, 78, who has held the post since 2006 and also is president of the cardinal committee that oversees the Vatican Bank, had been expected to be replaced since it is common for new popes such as Frances to put their own imprint on the church's hierarchy, The New York Times reported.
Bertone will remain in office until Parolin takes over in mid-October, the newspaper said.
Parolin, 58, is the Vatican envoy to Venezuela and served as deputy foreign minister from 2002 to 2009. The Times noted he has handled a variety of Vatican diplomatic roles, including leading talks to improve relations with Vietnam.
Parolin said in a statement Saturday he was ready to begin "a difficult and challenging mission" overseeing the church's foreign policy, as well as internal church affairs, with his goal being "the good of the holy church, and the progress and peace of humanity, that humanity might find reasons to live and to hope."
Parolin will be a key player in the pope's efforts to end revamp the church's administration in the wake of the 2012 leaks scandal when the disclosure of confidential papal letters and documents disclosed infighting and other problems inside the Vatican, including at the Vatican Bank where the top officials resigned this summer following allegations of money laundering.
Bertone has been blamed by some for a breakdown in management that allowed the problems to occur, the Times said.
The Vatican said Saturday, however, the pope would publicly thank Bertone "for his faithful and generous service."