The 50-year-old Conceição has been given an 18-month contract by the Italian club.
Conceição, who played in Serie A with Lazio, Parma and Inter Milan, coached Porto for six seasons before stepping down in June.
His first match in charge of Milan will be against Juventus in the Italian Super Cup semi-finals in Saudi Arabia on Friday.
"The club extends a warm welcome to Sérgio and his staff, wishing a journey full of success and fulfilment." the Rossoneri said in a statement.
Conceição landed at Milan's Linate airport on Monday afternoon and reportedly headed straight to the club's training ground to meet the team and staff.
Fonseca's dismissal was announced on Monday morning after the Portuguese coach was informed following a 1-1 draw at home to Roma the previous night, which left Milan eighth in the standings, 14 points off leaders Atalanta and Napoli.
"Yes, it's true. I'm out," Fonseca told reporters when he lowered his car window as he left San Siro following Sunday's match. "That's life…I did everything I could."
Fonseca was hired in June and produced only 12 wins in 24 matches across all competitions. His last action as Milan coach was to be sent off for dissent in the first half of Sunday's match.
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