The Blues are favourites to win the Premier League after Mourinho welcomed a raft of talent - which also includes Cesc Fabregas, Filipe Luis and Didier Drogba - to West London, and Costa claims that Chelsea's "outstanding squad" can fulfil their potential.
"Joining was an easy decision for me. We have some of the best players in the world, the best manager in the world and it's a club with great history," he told reporters.
"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.
"We have an outstanding squad and, if we can all stick together, pull in the same direction and remain focused, I don't see any reason why we shouldn't be going to the final stages and fighting for every trophy available."
Costa will get his first taste of English football on Monday when Chelsea kick off their league campaign with a trip to Burnley.