Bolsonaro, meeting US Secretary of State Pompeo in Brasilia, said that the tendency for Brazil "to elect presidents that for some reason were enemies" of the US was over and now "it is just the opposite: we are friends."
Pompeo responded that Trump "is very pleased with the relationship that our two countries are on the precipice of beginning to develop."
Pompeo also told new Brazilian Foreign Minister Ernesto Araujo that the affinity between Trump and Bolsonaro "creates a truly transformative opportunity for our two nations," especially in terms of economic and security cooperation.
The glowing mutual appraisals came a day after Bolsonaro was sworn in as Brazil's new leader for the next four years. The 63-year-old former army captain - an avid user of social media and avowed enemy of "political correctness" who has a record of making misogynist and racist comments - used his first presidential speech to pledge a fierce combat against crime, corruption and leftwing "ideology."
His ascension marks Brazil's most dramatic lunge to the right since democracy was restored in 1985 following nearly 20 years of a military dictatorship that Bolsonaro served and has evoked nostalgically for the "order" it brought.
Bolsonaro has particularly railed against the leftist Workers Party, that ruled Brazil between 2003 and 2016 but which is reviled for a string of corruption scandals.
In his meeting Wednesday with Pompeo, Bolsonaro said "I would very much like to increasingly make up for" the distance Brazil had kept from the United States in the past.
Referring to Pompeo's army rank of captain from when he served in the US army in 1986-1991, Bolsonaro added: "I'm saying this as captain - two captains - from captain to captain, so we stand together."
Pompeo emphasized the "set of shared values" that should enhance ties.
Pompeo represented the US at Bolsonaro's inauguration. The dignitaries also included Israeli Prime Minister Benjamin Netanyahu - who spoke of his own "brotherhood" with Bolsonaro - and nationalist Hungarian Prime Minister Viktor Orban, among others.
While Brazil previously carved out an independent foreign policy under which it sought to be on friendly terms with all governments, the shift in alliances and geopolitical and economic strategy under Bolsonaro could carry significant implications.
Venezuela's Socialist government headed by President Nicolas Maduro in particular could feel squeezed between the sanctions-wielding US and an assertive Brazil. Brazil is already one of the main host nations for Venezuelans fleeing the economic collapse at home. It is also a major Latin American oil exporter, like Venezuela.
Bolsonaro has promised to do all he can to challenge the governments of Venezuela and Cuba, drawing him closer to Washington's stance.