Paraguay briefly moved its embassy, but reversed the decision months later.
Bolsonaro promptly thanked Trump, adding: "under God's protection, we shall bring prosperity and progress to our people!"
Also like Trump, the brash Bolsonaro has ruffled feathers both at home and overseas with his unequivocal support for Israel and his promise to move Brazil's embassy to Jerusalem.
The agreement came as Prime Minister Benjamin Netanyahu met with Honduran President Juan Orlando Hernandez and US Secretary Mike Pompeo on the sidelines of the inauguration of Brazil's President Jair Bolsonaro in Brasilia.
Tuesday's festivities in the capital of Brasilia began with a motorcade procession along the main road leading to Congress and other government buildings.
Netanyahu, seated alongside Pompeo, said the two would discuss "the intense cooperation between Israel and the United States which will also deal with the questions following the American decision on Syria".
Bolsonaro voters hope their man will do better.
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Bolsonaro, meanwhile, has said his education ministry will stop "Marxist trash" being taught in schools and universities - another swipe at the Workers Party, which greatly boosted access to education for the poor and blacks.
Leftist President Evo Morales of Bolivia, however, was invited and warmly embraced Bolsonaro after the ceremony.
Brazil only returned to democracy in 1985 after more than 20 years under military rule and some critics see his election as a threat to the country's democracy.
Bolsonaro plans to realign Brazil internationally, moving away from developing nation allies and closer to the policies of Western leaders, particularly U.S. president Donald Trump, who sent Secretary of State Mike Pompeo to his inauguration.
"We are counting on Congress to provide the judicial support so police can do their jobs", Bolsonaro said, signaling that he may soon submit legislation that would allow police to be tried outside the criminal system.
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.
"This inauguration is a turning point", said another, 36-year-old teacher Mauro Penna.
Netanyahu's Brazil trip came at a sensitive time for the leader, who is maneuvering to stay in power despite a slew of corruption allegations.