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.
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.
