In a meeting with Honduran President Juan Orlando Hernandez, Israeli Prime Minister Benjamin Netanyahu and US Secretary of State Mike Pompeo, "it was agreed to strengthen political relations and coordinate cooperation on development in Honduras", read a joint statement by Honduras, Israel and the US.
They were surrounded by dozens of guards on horses and plain-clothes bodyguards who ran beside the vehicle.
Once inside Congress, Mr Bolsonaro and his vice president, retired Gen Hamilton Mourao, took the oath of office.
Mr Bolsonaro is the latest of several far-right leaders around the globe who have come to power by riding waves of anger at the establishment and promising to ditch the status quo.
In his inauguration speech before Brazil's Congress, Bolsonaro called for "a true national pact between society and the executive, legislative and judicial powers" to restore the lackluster economy - "without ideological bias".
"Congratulations to President @jairbolsonaro who just made a great inauguration speech", the U.S. president tweeted. "The U.S.A.is with you!" "Together, under God's protection, we shall bring prosperity and progress to our people!"
Tens of thousands of people attended Bolsonaro's inauguration ceremony in Brasilia, which was held under tight security that included warplane patrols, anti-drone technology and multiple crowd barriers. Military tanks, fighter jets and even anti-aircraft missiles also were deployed.
The precautions were more stringent than in years past, in part because Bolsonaro survived a stabbing attack by a mentally unstable man when he was campaigning for the presidency in September.
On Sunday, the Prime Minister of Iraq, Adil Abdul-Mahdi, told reporters that a security delegation had met with Syrian President Bashar al-Assad in Damascus, and hinted at a bigger Iraqi role in the fight against the Islamic State (IS) in Syria as the USA plans to withdraw from the country.
Leftist Presidents Nicolas Maduro of Venezuela, Daniel Ortega of Nicaragua and Miguel Díaz-Canel of Cuba, deemed dictators by Bolsonaro, were uninvited by Bolsonaro's team after the foreign ministry sent them invitations.
The sole issue left to be worked out was the United States' quashing of a $500 million arms deal between Israel and Croatia.
While Bolsonaro enjoys sky-high approval ratings, many in Brazil fear his nostalgia for the military dictatorship that reigned from 1964 to 1985, his hardline approach to fighting crime and his record of disparaging women and minorities could herald a harsh shake-up.