The 63-year-old politician easily won the first round on October 7, finishing far ahead of the field with an overwhelming 48 percent.
Brazilians will also elect governors in 14 regions, including populous States like são Paulo and Rio de Janeiro.
Bolsonaro, who cast himself as a political outsider despite a 27-year career in Congress, is the latest of several leaders around the globe to gain prominence by mixing tough, often violent talk with hard-right positions.
Brazil's most polarized election since 1985 and the near-fatal stabbing of Bolsonaro at a rally a month ago have caused turbulence on markets, yet the real currency BRL= strengthened 9.7 percent against the dollar in last 30 days as his prospects of winning increased. "There's a light at the end of the tunnel".
Bolsonaro has declared he will move the Brazilian embassy to Jerusalem from Tel Aviv.
"That is why I'll vote for Fernando Haddad", Joaquim Barbosa, former chief justice of Brazil's Supreme Court and an anti-corruption crusader, tweeted Saturday.
Minutes after he was elected, several global human rights groups put out statements demanding that Bolsonaro respect Brazil's democracy. Several key endorsements late Saturday gave Haddad's camp hope that they could still pull out a victory.
Riot police separated supporters of Bolsonaro and those of his leftist rival Haddad when they briefly scuffled in Sao Paulo.
Jair Bolsonaro defeated Fernando Haddad of the Workers' Party, a leftist, handily in the final round of the presidential elections.
As only two candidates remain and those figures discard voters who say they will annul their votes, that in practice means Haddad needs to win 5 percentage points to overtake the right-winger.
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The player once dubbed "Captain Cool" retired from Tests in 2014 and then relinquished the limited-overs captaincy in 2017. Other significant announcements include the addition of Krunal Pandya and Washington Sundar for the six T20Is.
Bolsonaro, who ran on promises to clean up Brazil and bring back "traditional values", said he would respect the constitution and personal liberty.
The highly divisive Lula, who stands accused of masterminding the massive pilfering of state oil company Petrobras, was barred from running because he is serving a 12-year sentence for bribery.
The past few years in Brazil have been exceptionally turbulent.
The center-right leader took over from Lula's successor, Dilma Rousseff, after she was impeached in 2016 for financial wrongdoing in office, ending the Workers' Party's 13 years in power. The economy suffered a two-year recession and is only beginning to emerge, with growth stagnant and unemployment high. He also wants to let more Brazilians buy weapons to fight crime. There were numerous reports of politically motivated violence, especially directed at gay people, whom Bolsonaro has disparaged.
His numbers jumped by around 15% in September after he was stabbed in the stomach during a campaign event.
Trump trod a very similar path. "Bolsonaro is essentially saying, 'Fairness means that I win".
"For the first time in 32 years of voting, a candidate has made me afraid".
"All these people here are outraged, upset about corruption and crime, and we are with Bolsonaro".
As widely predicted, Jair Bolsonaro is the new president of Brazil after Sunday's balloting.
Bolstering his rebel image is his reputation for offensive statements and sometimes extreme views, including insulting women, black people and the LGBT community.
"We have the responsibility to mount an opposition, putting national interests, the interests of the entire Brazilian people, above everything", Haddad said.