The 17-year-old will swap Dinamo Zagreb for the Italian club after agreeing personal terms on a long-term contract earlier this afternoon.
Spurs had been consistently linked with a move for the central defender this summer, with reports in the Croatian media claiming that a fee had been agreed to sign Jedvaj and Alen Halilovic from Dinamo in a double deal.
Roma sporting director Zoran Mamic confirmed today that the Giallorossi's pursuit of Jedvaj had been successful, with the Serie A giants just waiting on international clearance.
Sky Sports News quotes him as saying: "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."
UEFA are expected to formally agree the transfer later this evening, with Jedvaj currently in Rome awaiting clearance to begin training with Rudi Garcia's side.