After stalling in the first three months of the year, the economy has now had two consecutive quarters of growth, the statistics agency said, steering clear of a recession that had seemed likely only months ago.
Gross domestic product expanded by 0.6 percent in the July-to-September period, compared with the revised 0.5 percent in the previous three-month period.
It rose 1.2 percent from the same quarter last year.
An initial reading showing the economy contracted by 0.2 percent in the first quarter has also been revised to zero.
The third-quarter figure beat expectations of analysts surveyed by the Brazilian economic daily Valor, who had predicted 0.4 percent growth.
Driving the acceleration was agriculture, industry and services, which grew 1.3 percent, 0.8 percent and 0.4 percent, respectively, from the previous quarter.
Bolsonaro tweeted that the results showed "we're on the right path," referring to the ambitious economic reforms his ultraconservative government has been pushing through Congress since taking power in January.
Bolsonaro's government and outside analysts both anticipate 1.0 percent growth for 2019, edging down from 1.1 percent in 2017 and a revised 1.3 percent in 2018.
That will be too little to put a dent in unemployment which currently affects 12.4 million Brazilians. But analysts expect stronger growth next year, and have raised their 2020 GDP estimates to 2.2 percent from 2.0 percent.
After cutting interest rates to a new historic low of 5.0 percent in October, the central bank said it expected "some acceleration" in growth in the fourth quarter.
The figures come after US President Donald Trump announced plans Monday to reimpose tariffs on steel and aluminum from Brazil and Argentina, apparently blindsiding Bolsonaro, who considers himself an ideological ally of the Republican leader.
Bolsonaro has sought to play down the issue, saying he would appeal to Trump for more understanding of Brazil's position and boasting he has an "open channel" with the US leader if needed.
A wave of protests sweeping across Latin America has slowed the pace of reforms in Brazil, Economy Minister Paulo Guedes indicated in a recent interview with Brazil's Globo.
"We were on a path. Then, suddenly, the confusion in Latin America started ... the political timing begins to change," Guedes said.