Torres moved to Stamford Bridge from Liverpool for £50 million in January 2011, a fee that represented the British transfer record prior to Angel di Maria's £59.7m switch to Manchester United earlier this week.
However, the Spain striker failed to exhibit his best form at Chelsea, scoring just 20 Premier League goals for the club in 110 appearances.
The Premier League club confirmed on Friday that a deal had been agreed with Milan, paving the way for Torres to spend the remaining two years of his existing Chelsea contract on loan at San Siro.
And Chelsea announced on Sunday that the formalities of the transfer have now been completed.
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