Roberto Andrade was left fuming at how the CBF orchestrated the arrival of the Timao boss, who becomes the nation's fourth coach in as many years
Dunga paid the price for two Copa America failures with the Selecao and a poor start to the team's World Cup qualifiers as he was sacked on Tuesday, along with coordinator Gilmar Rinaldi.
And while the Brazilian Football Confederation (CBF) is yet to officially announce his successor, Corinthians' Roberto Andrade let slip the move during a press conference.
"The professor Tite is no longer Corinthians coach, and he will not be in control for tomorrow [Thursday's] game," the president told journalists the day before the Timao face Fluminense.
"Cleber Xavier, Matheus, his son, and Edu Gaspar will also be leaving with him."
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Tite has enjoyed great success over three separate spells with the Sao Paulo club, winning two Serie A titles, the 2012 Copa Libertadores and Club World Cup among other titles.
But Andrade admitted he was furious at how his latest exit from the club had come about, pointing the finger at the CBF.
"I am p*ssed off with the CBF over the way they came to grab Tite from here. I never received a phone call from the president," he fired.
"Now, when it was already all worked out, he tried to call me. The national team does not deserve Tite, they are not used to dealing with ethical people as you can see by how the took him from the club.
"Tite should be thanked by everyone here for the work he has done. Corinthians have progressed a lot, and so has Tite."
The ex-Corinthians man thus becomes the fourth Selecao coach in the last four years, after Mano Menezes, Luiz Felipe Scolari and Dunga.