The news came as a complete surprise because Atletico Madrid assistant coach German Burgos said earlier in the day that Torres was all set to rejoin his boyhood club.
"It is on the verge of completion and we are waiting for things to firm up," Burgos said of the deal.
"He will be a very important reinforcement for the second half of the season," Diego Simeone's number two told Spanish media.
Chelsea made the announcement about Torres' permanent switch to Milan on their website.
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"The striker moved to the San Siro on a two-year loan deal in August and on Jan. 5 he will complete a permanent transfer to the Serie A side," said the Stamford Bridge club.
"Chelsea Football Club thanks Fernando for his service during the past four seasons and wishes him the very best for the future."
Torres, who joined the Londoners for a British record fee of 50 million pounds ($77.75 million) in January 2011, had a chequered spell at the club but helped Chelsea win the Champions League and the FA Cup in 2012 and the Europa League a year later.
(Writing by Tony Jimenez, editing by Pritha Sarkar)
