Critics of Bolsonaro are anxious that the former army captain, who has expressed nostalgia for the years Brazil was under military rule, may curtail citizens' freedoms and undermine Brazil's constitution.
Bolsonaro, 63, will take office on January 1.
Prime Minister Benjamin Netanyahu called Brazil's president-elect Jair Bolsonaro on Monday night, congratulated him on his election victory and said it would surely lead to a strengthening of ties between Israel and Brazil.
Sitting next to his wife and wearing a dark blazer, the longtime congressman delivered his speech in a stern voice.
"We can not continue flirting with communism".
Bolsonaro's election was met with dismay by thousands of protesters, who poured into the streets of São Paulo and other cities-and were met by riot police-after the results were announced. "For the first time I feel represented", Andre Luiz Lobo, 38, told AFP news agency. Instead, support coalesced around Bolsonaro, who both is and isn't an outsider: He has served for almost three decades in Congress, but he has often been at the margins of that institution and he painted himself as just the strong man Brazil needed to dismantle a failing system.
A major pro-government, far-right Hungarian news outlet compared him to Trump and chastised the mainstream media for criticizing Bolsonaro's campaign.
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Aides said Haddad, 55, had not called Bolsonaro to congratulate him.
"Fascists!" shouted tearful supporters at the headquarters of Haddad's Workers' Party in Sao Paulo.
Despite his polarizing nature, Bolsonaro maintained a strong degree of support as many in the country seek to move away from the Worker's Party, which has ruled Brazil from 2003 to 2016 and has been blamed for leading the country into poverty and corruption.
"It is important to enact, with dialogue and tolerance, reforms to improve the economy and the integrity of the public administration, as well as restoring the population's confidence in the political class", Judge Sergio Moro wrote in a statement.
"This is a dark day for Brazil".
"Canada and Brazil enjoy a deep relationship. numerous relationships between people and businesses, as well as. our close cooperation on security and defence, agriculture, education, technology and innovation", she said.
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His opponent Mr Haddad had warned on Sunday that democracy and freedom were "at risk" in the election, echoing widespread fears that a Bolsonaro win would spell disaster for human rights and civil liberties.
Have the right to vote more than 147 million voters. Bolsonaro's history of disparaging remarks is more widely known, including saying he would not love a gay son and would rather he died and telling a fellow member of Congress, a woman, "I would never rape you because you do not deserve it".
But for a majority of Brazilian voters that did not eclipse the appeal of a man seen as promising radical change, in a country mired by years of political corruption, violence and an economic recession.
Incidentally, both - USA and Brazil - are now ruled by conservative populists promising to overturn the political establishment.
Brazilians have elected strident far right populist Jair Bolsonaro to be their President, making the most radical political choice since the return of democracy in 1985.
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