The 25-year-old, who gained Spanish citizenship in the summer, signed the necessary documentation on Tuesday that will allow the forward to play his international football for the World and European champions.
"It was a difficult decision for all involved, to decide between the country of your birth and the country that has given you everything, which is Spain," Costa told Atletico's official website.
"I have considered it and the right thing is to play for Spain because here is where I have achieved everything. All that I have in my life has been given to me by this country, who I have a very special affection for. Here I feel appreciated for what I do every day and feel the love of the people.
"I want people to understand that at no moment have I turned down Brazil. That is not how I see it. I simply feel valued here, where I have made my career. All that I am I owe to this country."
"It has been a well-thought out decision, but there has been no rejection. I have family in Brazil, it is where I was born and where I will live when I stop playing football. Hopefully people will understand and respect that."