Italy midfielder Montolivo spent seven seasons at Fiorentina, captaining the side, before joining Milan at the start of this term.
Seen as a player who has never quite lived up to his early promise, the 28-year-old intially found the going tough as Milan's rebuilt team floundered, but he has become a driving force at his new club.
"I didn't realise he was so good, he can become the leader of this team for many years," team-mate Massimo Ambrosini told Milan's website.
"In life and in professions, relationships can break down and not always in an understandable and painless way for everyone," Montolivo wrote in an open letter to Fiorentina supporters after leaving the club.
"Although some see me as an enemy, I can only wish joy and satisfaction to Fiorentina, Florence, to my former comrades and all the people who work every day in the club with passion and dedication."
Fiorentina's revival, in their first season under coach Vicenzo Montella, has been one of the season's high points, and has included a 3-1 win away to Milan and a 4-1 thrashing of Inter Milan at home.
However, they could ultimately pay for some disappointing performances, such as a home defeat to bottom club Pescara and last week's 2-1 loss at Cagliari.
"It will be difficult without him and we'll certainly be lacking something, but there are other players in the squad who want to make their mark," said winger Juan Cuadrado.
Milan are third in Serie A, which would earn them a place in next season's Champions League play-off round, and Fiorentina are six points adrift of them in fourth, which would send them into the Europa League.
Anything other than a win is likely to end Fiorentina's hopes of returning to the Champions League for the first time since 2009/10.
"The next three games will be decisive," said Napoli forward Marek Hamsik.
