Thousands of the far-right president's supporters gathered at a stadium in Rio de Janeiro, where he was nominated.
He promised to retain a welfare programme that makes cash payments to poorer Brazilians.
His left-wing rival, Luiz Inácio Lula da Silva, is widely known for his policies to lift people out of poverty.
Mr Bolsonaro's candidacy was officially endorsed by his right-wing Liberal Party. The election is due to take place on 2 October.
During the rally at Maracanãzinho stadium, Mr Bolsonaro told his supporters, "The army is on our side."
"It's an army that doesn't accept corruption, doesn't accept fraud," he added. Gen Walter Braga Netto, former defence minister, has been nominated as Mr Bolsonaro's vice-president.
Lula, who previously served as president from 2003-10, was officially nominated by the left-wing Worker's Party on Thursday. Some opinion polls suggest he leads Mr Bolsonaro by as many as 20 percentage points.