Spurs were believed to be keen on adding the 17-year-old centre-back to their ranks, but have been left empty-handed.
Instead, Jedvaj is set to embark on a new adventure in Italy.
Roma will complete the deal once they have received the necessary clearance from UEFA.
A statement released by Dinamo on their official website read: "Dinamo and Roma have agreed all the details of a move for Tin Jedvaj to the Italian club.
"The agreement has been found on Wednesday in Rome by sporting director Zoran Mamic.
"Dinamo and Roma agreed to the move of the player, who has remained in Rome.
"It is only missing international authorisation, which usually takes a couple of days. The two clubs have agreed on everything."