The Brazil-born Spain striker joined the Blues from Atletico Madrid, who he helped to a first Primera Division title in 18 years, breaking the duopoly of Real Madrid and Barcelona.
Jose Mourinho's Chelsea are chasing a first Barclays Premier League crown since 2010 when the new season kicks off next month.
Costa carries a heavy burden, with Mourinho bemoaning his strikers last term and Chelsea's forward recruits having a history of struggling to make a prolonged impression, Didier Drogba aside.
Costa told Chelsea TV: "I'd say to the fans that you need to be confident that I personally will fight for this club to make sure we are in contention to win as many trophies as possible
"I'm part of a great group here of players and we will do everything we can to give the fans what they want - and that's titles."
Source : PA
Source: PA