The summer signing from Atletico Madrid is due to be introduced to the club's fans tonight when the team faces Real Sociedad in a friendly at Stamford Bridge.
Following his arrival in West London, Costa hopes that he can win over the Chelsea faithful with his performances this season.
"I hope my actions on the pitch and my feet will do the talking and then people can decide if I'm a good player or not," he is quoted as saying by Sky Sports News.
"All I can say is I love playing hard and fairly. I want to improve, not only as a player but as an individual, and I believe this is the perfect place for me to do that."
Costa scored 35 goals in 44 games last season as Atletico won the La Liga title and reached the Champions League final.