"Chelsea Football Club thanks Fernando for his service during the past four seasons and wishes him the very best for his loan in Italy," Chelsea said in a statement on their website.
Torres, 30, signed for Chelsea for a then British record 50 million-pound deal from Liverpool in 2011 following a hugely successful spell at Anfield in which he was regarded as being among the best forwards in the world.
He never reproduced that form for Chelsea but did score a memorable goal in their Champions League semi-final win over Barcelona at the Nou Camp.
"When you play for Milan there are always big expectations. After a difficult season, all the players and the fans want to get back into the Champions League and fight for trophies," Torres told Milan's website.
"It will be a nice challenge trying to get back into the top-three in the league and subsequently have the chance to play in the Champions League next year."
Torres won the Champions League, Europa League and FA Cup during his time at Chelsea.
(Reporting by Tom Hayward, editing by Ed Osmond)
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