Trump predicted he and Bolsonaro - who's been described as the "Trump of the Tropics" - would have a "fantastic working relationship", telling reporters as he opened the joint press conference that they have "many views" in common.
Brazilian President Jair Bolsonaro "has done a very outstanding job, ran one of the incredible campaigns; somebody said it a little bit reminded them of our campaign, which I'm honored by", Trump said as he and his fellow pro-business populist sat for pictures in the Oval Office.
Mr Bolsonaro has made clear he wants to strengthen military and economic ties with the United States, and Mr Trump appeared eager to deliver, announcing he would back Brazil's efforts to join the Organisation for Economic Cooperation and Development (OECD).
Trump has said he will take the US out of the Paris climate deal, while Bolsonaro has suggested he could lead Brazil out of the agreement, too.
Bolsonaro, who was critical of China in his campaign, announced hours after meeting Trump that he will visit the country in the second half of the year. "So, what they do, like most people do when confronted with failure, is they hit their head against the wall even harder".
That also includes steps that would allow United States commercial space launches from a site in Brazil and increased trade between the two countries.
"For the first time in a while, a pro-America Brazilian President arrives in DC", Bolsonaro tweeted as his trip began on Sunday.
"Nowadays, you have a president who is a friend of the United States who admires this attractive country", he said.
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There is the possibility of an all-Premier League final, with the winners of Arsenal's tie at home to Villarreal or Valencia in the first leg of the semifinals.
Trump later told reporters he intends to work to designate Brazil a "major non-NATO ally" and "maybe a North Atlantic Treaty Organisation ally" as well.
The two also share a penchant for family politics, employing relations as some of their closest advisers.
In an interview with Fox News Monday, Mr Bolsonaro said he supported Mr Trump's immigration policies and his efforts to build a wall along the US-Mexico border.
Trump said Tuesday that "we don't want to say exactly" what he would like to see happen next in Venezuela, where he has repeatedly said he reserves the option of a USA military intervention to unseat Maduro.
Trump commented that he was glad that their supporters could see through the bias provided by old media and social media. "It's the beginning of a partnership focused on liberty and prosperity, something that all of us Brazilians have long wished for". Trump praised Brazil for recognizing Juan Guaidó as Venezuela's interim president and supporting the United States in providing humanitarian aid to Venezuelans.
"We call on members of Venezuelan military to end their support for Maduro who is really nothing more than a Cuban puppet and finally set their people free", Trump said.
"No Brazilian president had ever paid a visit to the Central Intelligence Agency", said Celso Amorim, who served as foreign minister under former President Luiz Inacio Lula da Silva and is a Bolsonaro critic.
Eduardo, Bolsonaro's youngest son and a member of Brazil's Congress, is accompanying his father on the US trip.