The Atletico Madrid striker has already made two appearances for the Selecao but, given both games in which he featured were friendlies, he is free to play for la Roja having secured Spanish citizenship in July.
Costa was called up by Brazil for this month's friendlies against Honduras and Chile but, on Tuesday, he formally declared for Spain, much to the annoyance of Scolari who immediately dropped the forward from his latest squad.
"A Brazilian player who refuses to wear the shirt of the Brazilian national team and compete in a World Cup in your country is automatically withdrawn," Felipao said in a statement.
"He is turning his back on a dream of millions, to represent our national team - the five-time champions - in a World Cup in Brazil."
Brazilian's Football Association (CBF) president Jose Maria Marin has already stated that he intends to "fight until the end" to secure the services of Costa, who is currently La Liga's top scorer.