The 17-year-old, who had been linked with European giants such as Arsenal and AC Milan, will move to the Italian capital for a transfer fee of €5 million.
Giallorossi director Italo Zanzi released a statement via the club's official website confirming the completion and revealing that the young Eastern European has signed until 2016.
The statement read: "AS Roma announce that we have agreed a deal with GNK Dinamo Zagreb for Tin Jedvaj for a sum of €5m.
"The Croatian player has signed a three-year contract with us, which will expire in 2016.
Jedvaj, who follows Mehdi Benatia and Maicon in bolstering Rudi Garcia's defence, namechecked Thiago Silva and David Luiz as two of his idols and claims he fears no forward in Serie A.
He added: "The attackers are very strong in Italy, but I'm not afraid of anyone on the pitch. I think my strengths are my technical skills and my positional sense on the pitch.
"As role models, I have Thiago Silva and David Luiz. I'd like to be like them, because they are sure of their own ability."