BRASÍLIA—Jair Bolsonaro was sworn in Tuesday as Brazil’s first right-wing president elected since the end of military rule three decades ago, vowing to restore order to a country hobbled by crime, corruption and a deepening fiscal crisis.

The fiery ex-army captain, who is recovering from a near-fatal stabbing during the election campaign, rode in an open-top Rolls-Royce under heavy security to Congress, where he formally took office in a ceremony boycotted by swaths of left-wing politicians.