The 17-year-old defender was unveiled by the club on Monday after completing a move worth 5 million euros ($7.17 million), signing a three-year contract in the Italian capital.
Interest in Jedvaj had been high, with many clubs across Europe's top leagues keen to acquire his services, and it was Roma which convinced Jedvaj to leave Dinamo after just 13 appearances in the first team.
In a statement on the club's website, Roma announced Jedvaj's arrival and chief executive Italo Zanzi was delighted to have agreed a deal for the youngster.
"AS Roma announce to have agreed with GNK Dinamo Zagreb a deal for the permanent acquisition of the player Tin Jedvaj for the sum of â‚¬5million," the statement read.
"The Croatian player has signed a three-year contract; it will expire on June 30, 2016."
It is the second signing in as many days for Roma, with Mehdi Benatia having been announced on Sunday, and Zanzi admitted this deal was looking towards the future rather than an immediate impact on the first team.
"We present a younger player with a great future, we are happy to be here with us," he said.
"For us it is important to create a team that you think about tomorrow and the purchase of Jedvaj this is the sign of our will."
Jedvaj knows that it will be tough for him to break into the first team immediately but has set his sights on winning trophies with the club after collecting a double in Croatia last season.
"My hope is to win the titles, to reciprocate the trust that the club has placed in me to express myself to the fullest potential and to bring the Roma in Europe," he said.
"This is a club with great history, great names in the field: one of the best in football history as Totti.
"The attackers are very strong in Italy, but I'm not afraid of anyone in the field. I think my strengths are the technical skills and the sense of position in the field.
"As a model I have Thiago Silva and David Luiz: I'd like to be like them, because they are sure of their own means."