The England Under-21 striker spent the second half of last season on loan at The Reebok and scored eight league goals in 12 appearances for Owen Coyle's club.
Coyle made it clear he would like to keep Sturridge, but the former Manchester City player was determined to return to the Bridge.
The 21-year-old's decision came despite the tough competition for places at Chelsea, where £50million man Fernando Torres, Didier Drogba and Nicolas Anelka are expected to figure in the plans of Andre Villas-Boas.
Sturridge has yet to discuss in detail his role with his new boss, but the forward told Sky Sports News when asked if he sees himself as a Chelsea player: "Never any doubt.
"I'm here training in pre-season and looking forward to the start of the new season, where I can show everybody what I am capable of doing."
Sturridge is adamant he is happy to fight for a place and demonstrate his goalscoring ability to Villas-Boas.
He said: "It is the same in every team around the world. Every striker has got to fight for their place and it is no different here."
Sturridge added: "It is a thing every striker has got to be prepared to do. There are no guarantees in football at any club.
"It doesn't matter whether you are a star or not a star, you have to show the manager what you are capable of doing. Every season is a new season.
"The past is the past, in my opinion, so everyone has got to fight for their place."