Montella was presented to the media in a press conference on Thursday and declared his ambitions for the Rossoneri during his tenure.
Milan have endured a three-year absence from Europe's elite club competition, with their last appearance having come in the 2013/14 season.
"I'm extremely happy about being here. I perceive great responsibility and energy. I am enthusiastic and focused on work," he told the assembled press.
"It's unacceptable that Milan should have been out of the European cups for three years. Our objective is to return there."
Montella also spoke about meeting Milan president Silvio Berlusconi, who has returned to the office following heart surgery.
"Meeting him was a great emotion. He changed Italian football. I thought he looked to be in a good condition, he has great charisma so it was a good evening," the Italian added.
The 42-year-old could dip into the transfer market in an attempt to bolster his squad and improve on their dismal seventh-placed finish in Serie A last term.
"Milan have to play well. We have to lead by our style of play. That's what made Milan great over the years," he continued.
"We must promote an idea which both Milan and I believe in. To do that, we need the right players and of course I'll be giving some suggestions on the market.
"I speak with the club constantly. Now I must evaluate the players I already have, find out what kind of hunger and drive they possess. Then I'll see how well they fit into my plan."