25-year old Costa, who agreed to the switch to Stamford Bridge during the World Cup, is still on holiday following Spain's elimination from the tournament.
Despite failing to impress during the tournament, he still holds the reputation as one of the most promising strikers in Europe, having scored 27 goals in 35 games as Atletico Madrid won La Liga last season.
A move to the Blues has been on the cards for the duration of the summer, and, having confirmed the deal, Chelsea fans are delighted that they finally have a goalscoring striker who could potentially fill the still-vacant boots of club legend Didier Drogba.
And now it has been confirmed that Costa is set to join up with Chelsea this week, with Tuesday planned as the day for his arrival in London.
In an interview with globoesporte.com, the arrival was revealed, with Costa also announcing his delight at signing for such a 'great team'.
The Brazilian-born striker said: "Chelsea are a great team and the English Premier League is good to play in. I am hopeful for what is happening in my life and I will adapt well. It is a league in which I wanted to play for a long time and I think it will be a very good and fast adaptation."
Costa also confirmed, to his best knowledge, that he will be challenging Fernando Torres for the starting striker role in the first-team.
"It's always good to have competition. The important thing for a big club is having great players. Torres is a great player, I know I will fight hard to be among the starters and I like it. So I think it will be a clean and healthy competition."
Despite being delighted at the arrival of Costa, many Blues fans will be annoyed to see that Torres is likely to remain at the club - with the general consensus being that the Spanish striker does nothing for the club except taking his high wage.
However, if Costa can continue his scoring exploits into the new season, it may be that Torres never again appears in a blue shirt.