Atletico Madrid unveiled Fernando Torres to 45,000 fans at Vicente Calderon Stadium on Sunday with the striker targeting winning trophies.
Torres is re-joining the La Liga champions from AC Milan seven-and-a-half-years after leaving for Liverpool.
Torres, 30, said: "The club have grown and time has proved us right."
He added: "I have also won trophies, but I want to win trophies here.
"I was missing something to motivate me, something I could only find here.
"Off the pitch I have been through many things. On a personal level I am more mature and very happy to be here.
"On the sporting level things have changed too. At 24 I realised something very hard, that I needed to leave so that the club and I could grow.
"It was the most difficult moment of my career."
Analysis - Spanish football writer Andy West
It is difficult to overstate Fernando Torres's popularity with Atletico fans, who remember the deadly force of nature he was in 2007 rather than the misfiring disappointment of the last two or three years.
As much as his goalscoring exploits, Torres was loved because he was a boyhood fan who had progressed through the youth ranks and played with such obvious pride in the Atletico jersey.
Torres joined Serie A club AC Milan from Chelsea, who paid a then British record transfer fee of £50m to sign him from Liverpool in January 2011.
The Italian club confirmed a permanent deal for Torres, following its own initial two-year loan deal, during the Christmas period, but have loaned him to Atletico until the end of the season after Italy winger Alessio Cerci, 27, arrived from the Spanish side.
Torres, who scored 84 goals in 214 league appearances for Atletico from 2001-2007, could make his debut against Real Madrid in the first leg of a round-of-16 Copa del Rey tie on Wednesday.