The 63-year-old, a member of the Social Liberal Party and a former army captain himself, announced his choice of reserve general Hamilton Mourao on Sunday.
Mourao, of the conservative Brazilian Labor Renewal Party, told reporters it was “an honour and privilege to take part in the country’s reconstruction”.
Last year, Mourao controversially expressed support for a military intervention into politics in order to clean up Brazil’s mounting social problems, such as a spiralling murder rate and widespread high-level corruption.
Bolsonaro has also attracted criticism for making numerous controversial statements over the years regarding race, gender and sexual orientation.
In the lead-up to the October 7 election, he has pledged to crack down on crime and corruption.
Bolsonaro is projected to win between 19 and 22 percent of the votes, according to polling data published last week by research institute Data Poder 360.
Only former president Luiz Ignacio “Lula” da Silva polled ahead of Bolsonaro, with 31 percent, despite being convicted of corruption charges.
The 72-year-old, who ruled Brazil for two terms (2003-2010), was named as the leftist Workers’ Party candidate last week, but is likely to be barred from running in the election due to being found guilty of a crime.
A candidate must win a majority vote – 50 percent plus one – to secure an outright victory. Failing that, a second round of voting between the top two contenders will take place two weeks later.
“With the two-rounds format of the election, and a candidate requiring a majority share of the vote to win office, I don’t think Bolsonaro will be able to win,” said Professor Francisco Panizza, a Latin American politics expert at the UK’s London School of Economics.
He added, however, that the far-right candidate could gain enough support to enter a second-round vote.
“People have a sense politicians are not addressing their grievances and, if we have learned anything over the past few years, following the Brexit vote in the UK and the election of Donald Trump in the US, it’s that you can never make a safe prediction,” said Panizza.
Every presidential election in the country since 2002 has gone to a second round.
Lula’s running mate
Bolsonaro’s nomination of Mourao came as Lula’s Workers’ Party also announced the former president’s running mate – former Sao Paulo mayor Fernando Haddad.
Lula said Haddad was both his vice presidential candidate and campaign spokesperson until a final court judgment is made on whether the imprisoned politician is allowed to run for a third term in office.
O PT anunciou @Haddad_Fernando como vice na chapa de Lula. Ele será o porta-voz de Lula até o trâmite final da homologação da candidatura na Justiça Eleitoral, quando @ManuelaDavila assumirá a posição de vice na chapa, por indicação do PCdoB.
Fotos: Ricardo Stuckert pic.twitter.com/Vm1T5UxWnH
— Lula (@LulaOficial) August 6, 2018
Translation: Haddad will be the vice president and his spokesperson until the confirmation of Lula’s candidacy. Then Manuela d’avila will be the [candidate for] vice president because of a coalition between PT [Workers’ Party] and the PCdoB [Communist Party].
Brazilian law prohibits people with criminal convictions from standing for office within eight years of them being found guilty.
Lula was sentenced in August to 10 years in prison for accepting a seaside apartment as a bribe from Brazilian construction company OAS. In January, an appeals court unanimously upheld his conviction and increased the prison sentence to 12 years.
The final ruling on Lula’s candidacy is expected to be made on August 15, the date by which all parties must register their candidates with the Superior Electoral Court.
Since 2014, more than 150 business leaders, multinational corporations and politicians – including Lula – have been arrested or prosecuted as part a major corruption investigation known as Lava Jato, or Car Wash.