"Everything is going in the right direction and if it continues the same way they will be the team I play for next season," added the Brazil-born centre forward.
Atletico have said Chelsea will have to pay Costa's buyout clause of just over 40 million euros (£32 million).
"I have always wanted to play in the Premier League," added Costa. "(Chelsea) is one of the best teams in the world so there are a lot of reasons why I took the decision.
"Every league is different but none is easy. I will have to work hard to adapt to the Premier League style."
Costa's goals helped Atletico win their first La Liga title in 18 years last season and propelled them to the Champions League final, where they came within seconds of beating city rivals Real Madrid before going down 4-1 after extra time.
The 25-year-old, who netted 36 times in all competitions, would join up with Spain team mates Fernando Torres, Cesc Fabregas and Cesar Azpilicueta at Chelsea and compete with Torres for a place in manager Jose Mourinho's starting lineup.
Chelsea announced last week that Fabregas was leaving Barcelona to join the west London club, a return to the Premier League for the 27-year-old midfielder, who spent eight years at Arsenal.
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