The 25-year-old Spaniard is the first defender to be signed by Antonio Conte for Chelsea.
According to reports, Barcelona have agreed a deal with Lyon defender Samuel Umtiti.
Costa caught the world's attention after having a breakthrough season at the Vicente Calderon during their historic title winning campaign of 2013-14. He scored 36 goals for them in 52 appearances in that season before Chelsea snapped him up in the summer of 2014.
According to reports, Chelsea are looking to bring Lazio winger Antonio Candreva to Stamford Bridge in the summer.
According to reports, Juventus are now discussing personal terms with Borussia Dortmund play-maker Henrikh Mkhitaryan.
Serie A champions Juventus are reportedly eyeing Real Madrid midfielders Toni Kroos and Mateo Kovacic in a bid to add more technical ability to their midfield.
According to reports, Chelsea have reignited their interest in Fenerbahce's Simon Kjaer.