The Spain international, who arrived at Stamford Bridge from Liverpool for a reported £50 million in 2011, moved to San Siro on a two-year loan deal in August, but will become a fully fledged Milan player on January 5.
The news comes as speculation mounts surrounding a potential swap deal between Milan and Atletico Madrid involving Torres and Alessio Cerci.
The 30-year-old has endured a difficult three-and-a-half years with Chelsea, having struggled to live up to his sizeable price tag.
Torres scored 24 goals in 33 Premier League appearances during his first season with Liverpool after joining from Atleti in 2007, but only managed 20 in a total of 110 league outings for Chelsea.
Despite his struggles, Torres - a World Cup winner with Spain in 2010 - picked up winners' medals in the FA Cup, UEFA Champions League and UEFA Europa League during his time with Chelsea.
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