The 25-year-old scored eight goals for the Granata in the 2012-13 season and his industrious performances at the Stadio Olimpico were rewarded with an Italy call-up in March.
Cerci made his Azzurri debut from the bench against Malta later that month and is currently part of Cesare Prandelli's squad at the Confederations Cup.
A statement published on Torino's website on Thursday read: "Torino have resolved the co-ownership agreement concerning Alessio Cerci in our favour. The opposite deal has been done for (midfielder) Marko Bakic, who is now to all intents and purposes a Viola player."
Cerci made his league debut for Roma at the age of 16 in May 2004 but failed to break into the Giallorossi first team, spending subsequent seasons on loan with Brescia, Pisa and Atalanta before joining Fiorentina in 2010.