In a joint news conference in the White House Rose Garden, Trump said he told Bolsonaro he would designate Brazil a major non-NATO ally and possibly go further by supporting a campaign to make Brazil "maybe a North Atlantic Treaty Organisation ally".
Bolsonaro, who is a right-wing populist, praised Trump after he described past administrations as being "anti-U.S".
The Treasury Department also lifted sanctions on the wives of two Venezuelan TV magnates close to Mr.
Bolsonaro, a former army captain who styled his 2018 campaign on Trump's 2016 run, has declared himself on unabashed admirer of the us president and his politics and the American way of life. Mr Trump phoned Mr Bolsonaro within hours of him being declared the victor of October's election, during which he espoused loud pro-America - and pro-Trump - views.
Ahead of Tuesday's warm welcome at the White House, Bolsonaro said the United States and Brazil would sign an agreement permitting American satellite and rocket launches from Brazil's Alcantara space launch center.
It could also have large-scale implications for the future of efforts to slow or reverse global warming: Brazil is home to much of the threatened Amazon rainforest and Bolsonaro, like Mr Trump, is a climate change skeptic.
Bolsonaro, an outspoken foe of leftist ideology, said he had spoken to Trump about allowing the U.S. military to position itself in Brazil near the Venezuelan border.
At the outset of their first meeting, the two populist presidents exchanged football jerseys from their national teams, with Trump's name emblazoned on Brazil's famous yellow shirt and Bolsonaro's on the United States of America uniform.
Mr Trump later said he was "proud" to hear Bolsonaro adopt his hostile stance toward the news media.
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Bolsonaro, a former army captain, rose to power praising the US-backed military government that ran Brazil for two decades before a return to democracy in 1985, echoing cold war rhetoric in his presidential campaign about the need to fight a continued communist threat.
Bolsonaro's visit was not published on his agenda and members of the press were barred at the door while the president and his justice minister, Sergio Moro, hobnobbed with the spooks at the agency's Langley HQ.
He also congratulated Bolsonaro on his "tremendous" election victory, and said he expects they will work well together as they "have many views that are similar".
Trump said that he supports Brazil's effort's to join the Organisation for Economic Co-operation and Development, and is "very strongly" looking at US support for Brazil's effort to gain certain NATO privileges.
"The majority of potential immigrants do not have good intentions or do not intend to do the best or do good for the American people", he said.
Days after taking office on January 1, Mr Bolsonaro, a former army captain, said Brazil would consider letting the USA have a military base in the country as way to counter Russian influence in the region, particularly related to Brazil's neighbour Venezuela.
"We want to have a great America, yes, and we want to have a great Brazil, too", a smiling Bolsonaro said through an interpreter. In a joint statement, both leaders reiterated that they would stand with Guaidó, the democratically elected National Assembly, and the Venezuelan people.
"But we haven't done the toughest of sanctions yet", he said, adding that they may have to increase the sanctions against Venezuela.