"It was an easy decision for me to make," he said on chelseafc.com.
"We have some of the best players in the world, the best manager in the world and it's a club with great history.
"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. That's the reason I chose Chelsea and why I want to defend this shirt."
Mourinho wants Costa to perform the way he did for Atletico and the striker believes his attributes mean he is suited to the Premier League.
"One of the main things he (Mourinho) said was that he doesn't want me to change," added Costa, who scored 64 goals in 134 appearances for Atletico.
"It was Jose's and the club's decision to buy me and the reason they signed me was because of the way I played at Atletico.
"I don't feel I have to change much, I just have to improve fine details to become a better player, hopefully I will have a similar season to the last one."
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