The former Fiorentina ace is thrilled to have finally linked up with the Rossoneri and insisted they are still a top side, even after waving goodbye to some important players
The Rossoneri sold their two key men to Paris Saint-Germain earlier in July, while veterans Gennaro Gattuso, Clarence Seedorf, Filippo Inzaghi, Gianluca Zambrotta and Alessandro Nesta have all been released as the club look to revamp their squad.
However, Montolivo, who is one of the few acquisitions Milan have made so far this summer, expects the San Siro outfit to remain at the top and admitted he had long wanted to move to Lombardy.
"I do not think Milan are struggling," Montolivo told Gazzetta dello Sport. "Sure, the club have lost two phenomenal players.
"But they were a big club before Ibrahimovic and Thiago arrived and they will remain big even without them.
"Milan were in my destiny. I could have joined the club's youth ranks as a six-year-old, but my parents thought that I was too young and that I should stay closer to home.
"That is why I grew up in the Atalanta system, even though my father was a fan of Milan."
The former Fiorentina midfielder then sent a warning to coach Massimiliano Allegri after he played in front of the defence in the club's 1-0 friendly victory over Chelsea on Saturday.
Italy used the 27-year-old behind the strikers in the build up to Euro 2012, but the experiment was unsuccessful, and Montolivo reiterated that he has no interest in the role.
"Where do I see myself in the team? I can say where I do not see myself - as a trequartista," he added.