The two sides reached an agreement for the Spain international on Friday evening, with the forward now having completed a medical with the San Siro outfit and agreed personal terms.
The move brings an end to a difficult spell at Chelsea, with the former Liverpool forward having struggled for form and goals since completing a £50 million move to Stamford Bridge in 2011.
Torres managed to score just 20 times in 110 Premier League appearances for the Blues, but will now ply his trade with the Rossoneri until 2016 - upon which time his current deal with Chelsea expires.
"I'm really happy to have arrived in Milan," Torres told reporters after touching down in Milan. "I cannot wait to start this new adventure.
"I spoke to coach [Filippo] Inzaghi yesterday and I am really pleased to work with a coach like him. He was a great goalscorer and definitely understands what the role of a striker is. I am sure that he can teach me and help me a lot in this adventure."
Chelsea have already snapped up a replacement for Torres in the form of Loic Remy, who completed an £8.5 million move to Stamford Bridge from QPR on Sunday.
The two deals complete a dramatic transformation of Chelsea's frontline, with Jose Mourinho having ditched Torres, Romelu Lukaku, Samuel Eto'o and Demba Ba, and brought in Remy, Diego Costa and Didier Drogba.