The 22-year-old defender signed for Genoa from Bari in the close season in a part-ownership deal with Inter, who will now take his full registration for 12.5 million euros according to local media reports.
"On one hand I'm sorry to let a player like that go but, on the other hand, decisions have to be made," Genoa president Enrico Preziosi, who last year sold Diego Milito and Thiago Motta to Inter, told reporters.
"We can say we have found a mutually satisfactory agreement."
Ranocchia is set to train with the world, European and Italian champions when they resume work after the mid-season break on Wednesday with his move being made official when the January transfer window opens.
The centre-back, who made his Italy debut in November, will add depth to Inter's defensive options with Walter Samuel having been ruled out for the season with a knee injury.
Seventh-placed Inter, whose next Serie A game is at home to Napoli on January 6, have also been linked in the media with Udinese's Chilean forward Alexis Sanchez.
Ex-AC Milan coach Leonardo was named Inter boss on Friday after Rafael Benitez, who had publically bemoaned a lack of signings, left the faltering treble winners by mutual consent.
