Chelsea boss Jose Mourinho confirmed after his team's 6-3 victory over Everton that Torres had left the club to join Milan on a two-season loan.
Torres is out of contract at Stamford Bridge in 2016 and the conclusion of the deal could mean the end of what has been a turbulent spell with Chelsea.
The 30-year-old Spain international went through lengthy spells without scoring and has managed only 20 goals in 110 Premier League appearances since joining the club from Liverpool for a then British record £50million in January 2011.
Milan confirmed on Twitter that Torres had landed at the city's Linate Airport, where he was greeted by 200 fans, and they posted a picture of the player holding a scarf before announcing he was at the Madonnina Clinic undergoing his physical tests.
He told Milan Channel: "It’s an honour and a privilege to wear this shirt. I want to take the side back into the Champions League and perhaps stay here for many years.
"I know some of the players like Alex, Essien, Diego Lopez. Demetrio Albertini also spoke well of Milan and he’s a great friend of mine.
"I was close to joining Milan when I was at Atletico Madrid, but we’re talking about many years ago, a long time has since passed. I know the history of the club and it is illustrious. I want to make the fans happy. I couldn’t wait to arrive and start the new season. I have already spoken to the coach."
Milan coach Filippo Inzaghi is hoping he can help Torres rediscover his best from in Serie A.
"I've spoken to Torres even if he still has to do the medical," said the former Italy forward.
"I found out what kind of person he is and it all seems very positive. It is up to me to get him back to the levels he is capable of and I will study his best position."