The 25-year-old, who scored 36 goals for the Spanish league champions last season, is Jose Mourinho’s second high-profile signing of the summer following the £27m capture of former Arsenal captain Cesc Fabregas from Barcelona.
Brazil-born Costa played in Spain for eight years and elected to represent his adopted country at the current World Cup. He played just 126 minutes as the holders were eliminated at the group stage.
His arrival casts fresh doubt over the Chelsea future of the last big-money Spanish striker to arrive at Stamford Bridge, Fernando Torres, and Belgium’s Romelu Lukaku. Both are though to interest Atletico.
Uncertainty remains over goalkeeping options, however, with Thibaut Courtois expected to be recalled from a three-year loan to Atletico. That could trigger the end of Petr Cech’s decade between the posts, with reserves Mark Schwarzer and Jamal Blackman both handed new contracts.