The Giallorossi have an option to extend the loan deal for an extra year, at no extra fee, and to sign the player permanently for a fee of €11 million (£8.74m) for the 2016-17 season.
The 20-year-old joins La Maggica having played 15 times in the Super Lig for the Turkish champions last term, with 13 of those appearances coming from the bench.
Salih confirmed on Sunday that he would be travelling to Italy for a medical ahead of his move to the Serie A giants, who finished the 2013-14 Serie A season in second place.
“I am going for a medical with Roma,” he stated. I’ll return with my signature on the contract!”
The Turkey international arrives at the club on the same day that former England international Ashley Cole has also been confirmed as a new recruit for Rudi Garcia’s side.