The former Porto coach succeeds Paulo Fonseca, who was sacked by Milan on Monday morning.
Conceicao has signed a deal to the end of the season with the option for another year.
“I’m proud to take on this adventure. The emotions are temporary, because we have work to do,” Conceicao told Milan’s internal media channels. “We need a warm heart and a cool head to do our best and win matches. That’s what we want.
“We represent a great club on a global scale, and we have to be worthy of this great club.
“We don’t have much time, that’s absolutely not an excuse, but I have to do my best with the time at our disposal so that the players understand what they need to do, firstly as individuals but also as a team, to be the best that we can be every single game.
“There is no other option, there is a lot of work to be done here with the team. We’ll need a strong mentality and with good organisation and the players’ quality, we will do good things this year.
“Words are just words, I need to prove myself with results. For that, we’ll need a lot of work from everyone, not just from the players but also from the staff who make the Milanello facility what it is.
“We’re here to work. What I want to tell the fans is that we’ll work hard a lot and become a winning side and become a team worthy of this great club.”