The Blues and AC Milan announced the agreement of a two-year loan deal on Friday evening, taking the 30-year-old to the expiration of his contract in 2016.
The Rossoneri confirmed on Twitter on Saturday that Torres had landed at Milan's Linate Airport, where he was greeted by 200 fans, and posted a picture of the player holding an AC Milan scarf before announcing he was at the Madonnina Clinic undergoing his medical.
Torres told the Milan Channel he could not wait to get started working under coach Filippo Inzaghi after a frustrating and underwhelming three and a half years at Stamford Bridge.
"I'm really happy to have arrived in Milan," he said. "I can't wait to do the medical, meet the fans and my new team-mates.
"I cannot wait to start this new adventure. I spoke to the coach (on Friday) and I am really pleased to work with a coach like him. He was a great goalscorer and definitely understands what the role of a striker is. I am sure that he can teach me and help me a lot in this adventure."
Torres revealed he had nearly become a Milan player before leaving Atletico Madrid for Liverpool in 2007.
"I was close to joining Milan when I was at Atletico Madrid, but we're talking about many years ago," he said. "A long time has since passed. I've now finally arrived at Milan. Playing for Milan isn't easy. It's an honour and a privilege to wear this shirt. I want to give my best and help the side have a great season."
The Rossoneri endured a dismal Serie A campaign last term, finishing eighth, 45 points behind champions Juventus, and missing out on European competition for the first time in 16 years.
Head coach Inzaghi, who was promoted from the youth team at the end of last season following Clarence Seedorf's dismissal, faces a challenging task to restore Milan's pride, but Torres is relishing the prospect.
"When you play for Milan, there are always big expectations," he said.
"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. Then, why not try and win something already this year? I'm expecting good things from this season."
Much was expected of Torres when he arrived at Chelsea from Liverpool in January 2011 for what was a British record fee, but he fell well short of living up to his £50million price tag.
He now appears to have played his last match for the Blues, and has set his sights on being with Milan for "many years".
"I thank the fans for the welcome," he said. "Through the social network sites and my official website I've seen that they are as happy as I am. I am sure that it will all go well.
"I can promise that I will give 100 per cent and that with their help this experience will be fantastic and for many years, I hope."
Inzaghi, speaking at his pre-match press conference ahead of Sunday's Serie A opener against Lazio, backed Torres to help the Rossoneri get back to the top, should the deal go through as expected.
"It isn't yet official for Torres," the Milan head coach said. "If he joins it is because everybody thinks he can be a useful player.
"He is always the first to arrive to training and very professional. We are rebuilding and we are on the right path. One step at a time, we will get back to the top."
Chelsea boss Jose Mourinho spoke glowingly of Torres on Friday, before news emerged of his imminent exit, and Inzaghi too has been impressed by what he knows of the Spaniard so far.
"I spoke to Mourinho to find out about what kind of man Torres is," Inzaghi said. "He is a player that has scored lots of goals and you don't forget this all of a sudden.
"He has the right attributes from a human point of view and that is good."
Inzaghi preferred to concentrate on Lazio's visit to the San Siro than speculate as to any further acquisitions he may be looking to make before Monday night's transfer deadline.
"Apart from Torres, I don't think it is right to speak about the transfer market," he said. "I want to focus on the match. We want to do really well.
"My only thought is on this debut which I really care about, in our stadium and with our people. We want to win back the fans."