Chelsea agreed a deal with Atleti to bring the striker to Stamford Bridge a fortnight ago and the move has now been finalised.
Costa will add presence to a Chelsea forward line that misfired for large parts of last season.
Samuel Eto'o was Jose Mourinho's top-scoring striker with 12 goals in all competitions, although neither the Cameroon veteran, Fernando Torres or Demba Ba were able to reach double figures in the Premier League.
Costa, on the other hand, plundered 27 goals in La Liga alone last term, only Lionel Messi and Cristiano Ronaldo managed more.
His superb form at the Vicente Calderon resulted in a tug-of-war between Brazil and Spain for his services at international level, which the Europeans eventually won.
Despite having a goalless and unsuccessful FIFA World Cup, which Spain were eliminated from at the group stage, Costa is determined to make a big impact in the Premier League next term.
The 25-year-old told Chelsea's official website: "I am very happy to sign for Chelsea.
"Everybody knows it is a big club in a very competitive league, and I am very excited to get started in England with a fantastic coach and team-mates.
"Having played against Chelsea last season I know the high quality of the squad I am joining.
"I would like to thank everybody at Atletico who made me into the player I am, it was an incredible time for me, but now I am starting a new adventure and I hope to win many trophies with Chelsea."
Costa joined Atleti from Real Valladolid in 2010 and scored 64 goals in 134 appearances for the Madrid club.
