The 21-year-old Serbian refused to sign a new contract in Florence after it emerged both Roma and AC Milan were interested in his services, and the Giallorossi have now won the race to secure the playmaker on a four-year contract.
A statement published on Roma's official website read: "Roma have agreed a deal with Fiorentina to acquire the playing rights of Adem Ljajic, in return for 11million euros.
"The agreement also recognises the payment of up to 4million euros in bonuses relating to achievements of both Roma and the player.
"The player has signed a four-year deal which takes effect from today and expires on June 30, 2017."
The announcement followed Roma's decision to agree the sale of influential Argentina forward Erik Lamela to Premier League club Tottenham for 30million euros, plus 5m in bonuses.
Ljajic scored 16 goals in 85 appearances for Fiorentina across the four seasons that followed his arrival from Partizan in 2009.
He courted controversy when sarcastically applauding former Viola boss Delio Rossi in May 2012, an action which prompted the coach to punch his player.
A return of four goals from six games towards the end of the 2012-13 season inspired Fiorentina to open contract talks with the Serbian but, after a summer of stalling, he was left out of the team that beat Catania on Monday due to the impasse.