The 25-year-old was scheduled to be in Washington preparing for the World Cup with the rest of Del Bosque's Spanish squad, but if reports are to be believed Costa has this afternoon passed a medical at Stamford Bridge.
The news comes as some surprise after Diego Costa suffered a torn hamstring only last month with many believing the forward would subsequently miss the World Cup.
Costa was a shock starter for Atletico in the Champions League final in Turin, but lasted only seven minutes before he was substituted.
The powerful 6"2 striker was a valuable cog in Diego Simeone's remarkable achievements at Atletico Madrid this season and after winning the Spanish title, Costa will leave La Liga on a high despite his last appearance coming in a defeat to fierce rivals Real Madrid in the Champions League final.
With this deal Chelsea will secure the first of a reported three targets all from Atletico Madird. Jose Mourinho is also thought to be keen on signing defender Filipe Luis and bringing former Blues midfielder Tiago back to Stamford Bridge.
Chelsea were short of fire power in attacking areas last season and a poor goal return from Samuel Eto'o, Fernando Torres and Demba Ba arguably cost Mourinho's side the title.
The Portuguese coach was never afraid to criticise his under-performing centre forwards and will no doubt fast track Diego Costa straight into the Chelsea first 11, with Fernando Torres and Samuel Eto'o tipped to leave Chelsea this summer.
Costa registered 36 goals in 52 for Atletico Madrid last season, and could hold the key for Chelsea's title hopes in the upcoming Premier League season.
On a good news day for Chelsea, Eden Hazard looks set to stay after being handed the number 10 shirt and it appears he will be lining up next to who has arguably been one of the best strikers in the world over the past 12 months.