Dilma Rousseff, 68, was addressing the nation on TV for the first time since senators voted overnight to suspend her for budgetary violations and put her on trial.
She vowed to fight the “injustice” by all legal means.
Vice-President Michel Temer has now officially taken over as interim leader and has appointed a team.
Respected conservative Henrique Meirelles, who headed the central bank under leftist ex-President Luiz Inacio Lula da Silva, becomes finance minister.
Michel Temer will serve while Dilma Rousseff’s trial takes place. It may last up to 180 days, which would mean Dilma Rousseff would be suspended during the Olympic Games in Rio de Janeiro, which start on August 5.
Brazil’s senators had voted to suspend her by 55 votes to 22 after an all-night session that lasted more than 20 hours.
Dilma Rousseff is accused of illegally manipulating finances to hide a growing public deficit ahead of her re-election in 2014.
In her TV speech, flanked by ministers at the presidential palace, Dilma Rousseff said that she may have made mistakes but had committed no crimes, adding: “I did not violate budgetary laws.”
She said: “What is at stake is respect for the ballot box, the sovereign will of the Brazilian people and the constitution.”
Branding the process “fraudulent” and saying her government was “undergoing sabotage”, Dilma Rousseff vowed to fight the charges against her and said she was confident she would be found innocent.
She accused the opposition of leading the impeachment because they had vehemently opposed all the advances she and her predecessor, Luiz Inacio Lula da Silva, had made for the Brazilian poor and lower middle classes.
After her speech, Dilma Rousseff left the presidential palace and shook hands with supporters lining the pathway.
In another speech outside Dilma Rousseff told supporters she could feel their “love and energy” on what she called a “tragic” day for the country.
Meanwhile, Michel Temer has nominated a 21-strong cabinet.
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