Drogba left Stamford Bridge for Chinese side Shanghai Shenhua last month after an eight-year stint in West London during which he scored 157 goals.
The Ivory Coast striker marked his exit in style by netting a late equaliser and the winning penalty in a shootout against Bayern Munich in the UEFA Champions League final as Chelsea lifted the trophy in May.
Torres has struggled for consistency since joining the Blues from Liverpool for a British record transfer fee of £50million in January 2011.
But the 28-year-old striker, who helped Spain to success at Euro 2012 this summer, is certain he can fill Drogba’s shoes.
“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 official 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 is aware of the expectation on Chelsea this season after they ended their much-publicised hunt for European glory and insists he and his team-mates are raring to go.
“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 said.
“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.”
Torres is looking forward to linking up with Chelsea’s new signings, with the club having made three captures so far in Eden Hazard, Marko Marin and Oscar.
“We are really happy and looking forward to the season,” he said.
“In pre-season we need to show we want to be part of the team, there are lots of new players coming in and we hope after the Olympics we will start working together fully. Different players have come, so it’s exciting for us.”