Jedvaj, 17, had been linked with Spurs for several weeks, but has elected to join the Serie A club for £4.3 million.
"Roma has made an agreement with Dinamo Zagreb to acquire full economic and sporting rights for football player Tin Jedvaj," the Italian club said in an announcement to the Stock Exchange.
"An upfront payment of five million euros has been made. The Croatian player has signed a three-year contract, which ends on June 30 2016."
It is unknown whether Spurs made a formal bid for the youngster, who played 13 first-team matches in the Croatian top flight last season, scoring once.
He has been capped by his country at U19 level.
- Sports & Recreation
- Dinamo Zagreb
- Tin Jedvaj