The Brazilian international, who is currently preparing for the World Cup, had a sensational 2013/14 campaign, finishing behind only Cristiano Ronaldo and Lionel Messi in the league goalscoring charts to help fire his side to the title. He was also key in their run to the Champions League final last month, where they fell at the final hurdle against Real Madrid.
Chelsea were short of striking options last season and have wasted no time in adding more firepower to their squad by wrapping up a deal for Costa. The Blues will pay £32 million for his services and could announce the deal shortly now that a medical has been completed.
According to the Guardian, Chelsea boss Jose Mourinho views the 25-year-old as the perfect solution to his problems, not only because of his goals but also because of his intensity and work-rate.
Eto'o will leave the club shortly when his contract expires, while there are doubts over both Torres and Ba's future at Stamford Bridge.
Costa could be the first player to make the switch from Madrid to London, with Chelsea keen on wrapping up deals for full-back Filipe Luis, as well as their former midfielder Tiago.