He has promised to reduce state intervention in the economy and indicated that Brazil could pull out of the 2015 Paris Agreement on climate change.
He takes over on 1 January 2019.
Is there a chance Mr Bolsonaro could soften his stance, now he’s won power? Few experts believe it. You only need to look to another firebrand in the continent for guidance.
“The things that Donald Trump outlined and the signals that he gave during the campaign he carried through with,” says Kyle Pope of the Columbia Journalism Review, who has studied parallels between Brazil’s new president and the leader of the US.
Many say a comparison with Mr Trump is inaccurate. Instead, they say Mr Bolsonaro is more akin to Rodrigo Duterte of the Philippines.
Whatever the comparison, what is clear is that country’s sharp swing to the right will resonate beyond Brazil as another populist takes power.
And the opposition will redouble efforts not to take away the gains that country’s made since it returned to democracy 30 years ago.
The future looks messy for Brazil.
Yes and no.
On the one hand, his PSL party achieved a remarkable breakthrough in this month’s legislative election, increasing its representation from one to 52 seats in the lower house.
However Mr Haddad’s PT remains the largest party, with 56 seats.
But most ominously for Mr Bolsonaro, there will be a record 30 parties represented in the next Congress.
This suggest that finding backing for legislation could be difficult for the new president.
What about reaction from outside Brazil?
A number of Latin American leaders congratulated Mr Bolsonaro:
Argentine President Mauricio Macri described the poll results as Mr Bolsonaro’s “triumph”
Chilean President Sebastián Piñera congratulated Brazilians for a “clean and democratic election”
Colombia’s Ivan Duque welcomed the result and called for the two countries’ “brotherly relations” to be strengthened further
Mexican outgoing President President Enrique Peña Nieto hailed Brazil’s “democratic strength”
Peru’s Martin Vizcarra wished Mr Bolsonaro “full success”
Venezuela’s Nicolás Maduro extended his “congratulations to the people of Brazil”
Amnesty International said that taking into account his campaign pledges, Mr Bolsonaro’s victory could pose a “huge risk” to Brazil’s indigenous peoples, LGBT communities, black youth, women, activists and civil society organisations.