Forward Andre Silva has moved the other way, too, with the Portuguese striker reportedly having overcome initial issues when completing his medical with the Bundesliga side.
Earlier in August, Eintracht had voiced hope that Rebic would remain despite interest from the San Siro side, with sporting director Bruno Huber claiming they were “still optimistic” of retaining his services.
However, the Croatia international had come in for criticism following a poor performance in the first leg of the Europa League qualification play-offs against Strasbourg, in which he was substituted at half-time.
After the match, Rebic was told by Eintracht head coach Adi Hutter that if he wished to remain with the club, he needed to show it on the pitch .
Rebic was then left out for the 2-1 loss to his former club RB Leipzig, but returned to the XI in the second leg against Strasbourg.
Frankfurt picked up a 3-0 victory and progressed through to the knock-out stages, but a red card for Rebic has ended his latest spell at the club.
Rebic will make a return to Serie A, having first featured in the Italian top-flight with Fiorentina after a €4.5m move from Croatian slide Split in August 2013.
However, Rebic struggled to break into the Fiorentina squad and ended up spending time on loan with Hellas Verona before heading to Eintracht on a temporary basis in 2016.
The forward has spent the last three seasons with Eintracht, the loan being made permanent in 2018. He has 17 Bundesliga goals during his time there, with his personal best of nine coming last season.
Eintracht have already suffered heavy losses in their attack this transfer window, having previously sold Luka Jovic to Real Madrid and Sebastien Haller to West Ham.
The 25-year-old started alongside fellow countrymen Luka Modric, Ivan Perisic and Mario Mandzukic in the 2018 World Cup final, in which France defeated Croatia 4-2.
Frankfurt sit seventh in the Bundesliga with two wins and a loss, three points behind leaders RB Leipzig, and will face Arsenal, Standard Liege and Portuguese side Vitoria SC in this season's Europa League.