The 30-year-old 2010 World Cup winner will now play for the Serie A side following three-and-a-half years at Stamford Bridge, in which time he helped Chelsea lift the Champions League, the Europa League and the FA Cup.
"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 is hoping the move to Italy will rejuvenate his career and told Milan's website: "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.
"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."
The Spain international joined Chelsea from Liverpool in January 2011 for a then British record transfer fee of £50million and will be out of contract at Stamford Bridge in 2016.
The former Atletico Madrid star struggled to capture the same form at Chelsea that had at times electrified Anfield and had seen him regarded as being among the best forwards in the world.
He went through several lengthy spells without scoring and managed only 20 goals in 110 Premier League appearances for the Blues.
He did, however, score 22 goals in the 2012/13 season spread over seven different competitions, a Chelsea club record.
And his highlights include his Champions League semi-final breakaway goal against Barcelona at the Nou Camp and the goal that helped beat Benfica to lift the Europa League trophy a year later.
For Spain, while at Chelsea, he helped his country to a second successive European Championship in 2012, securing the Golden Boot in the process thanks to his three goals, one of which was in the final where he also teed up club-mate Juan Mata to put the icing on a 4-0 win over Italy.
In the Europa League he scored key goals against Steaua Bucharest and Rubin Kazan before his opener in the final in Amsterdam.
He also netted Chelsea’s final goal of last season, a late winner at Cardiff, having earlier in the season raised the roof at Stamford Bridge with an even later goal that defeated Manchester City in the 90th minute.
Milan could make a second signing from Chelsea on Monday with Dutch midfielder Marco van Ginkel, 21, poised to complete a season-long loan deal after flying out to Italy on Sunday evening.
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