The 26-year-old managed just six goals in 32 appearances in his first full season in west London after completing a £50m switch from Liverpool to Stamford Bridge in January 2011.
Blues legend Drogba opted to leave the Champions League winners earlier this summer, with the Ivory Coast international linking up with his former Chelsea team-mate Nicolas Anelka at Chinese outfit Shanghai Shenhua.
“I am looking forward to it. I like the responsibility and it’s a thing I’ve been doing all my life,” Torres told Chelsea’s website.
“I think Didier did everything for this club, scoring the winning goal in the Champions League was an inspiration for us.
“Our relationship was great and I was talking to him when he decided to leave he wished me all the best and hopefully one day Chelsea fans will remember me as they are going to remember him.”
Torres, who was a second-half substitute in Chelsea’s victory over Bayern Munich on penalties in the Champions League final, is predicting another successful campaign at Stamford Bridge.
“It was an amazing summer for us, especially for Juan Mata and me who won the Champions League with the team and then were with the Spanish team and won in Europe, which means everything,” he added.
“We know we have big expectations this season, there are a lot of trophies to win and we are ready for the challenge. I am sure it is going to be a good season.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news