Standing side-by-side in the White House rose garden, Mr Bolsonaro told Mr Trump the USA and Brazil stood together in support of "liberties" including "traditional family lifestyle" and "against the gender ideology or the politically incorrect attitudes and against fake news".
US officials hope the visit will not only boost their economic relationship but align efforts to provide humanitarian assistance to Venezuela. Both are fierce critics of Venezuela's socialist President Nicolas Maduro.
Trump also said he supported Brazil's efforts to join the Organization for Economic Cooperation and Development (OECD), a club of the world's advanced economies.
To improve business relationships, both countries agreed to revive the U.S. -Brazil CEO Forum and start a new U.S. -Brazil Energy Forum.
"I'll have to talk to a lot of people but maybe a North Atlantic Treaty Organisation ally, which will greatly advance security and cooperation between our countries", he said. "There's zero hostility with me".
Bolsonaro's first trip overseas for a bilateral meeting since taking over as president in January is a sign of his desire to strike a new alliance between Brazil and the United States, the two largest economies and most populous nations in the Americas.
Becoming a "major non-NATO ally" implies a status upgrade that gives a country preferential access to the purchase of US military equipment and technology.
That statement was roundly criticized, including by former military members of his government, and the administration backed off.
When talk emerged last autumn of a "Trump of the Tropics" running for president in Brazil, the actual US President took keen interest.
"For the first time in a while, a pro-America Brazilian President arrives in DC", Bolsonaro tweeted as his trip began on Sunday. "It's the beginning of a partnership focused on liberty and prosperity, something that all of us Brazilians have long wished for".
Bolsonaro was scheduled to speak to the U.S. Chamber of Commerce later Monday.
Just ahead of the meeting between the two leaders, the United States and Brazil signed an agreement to support American space launches from Brazil.
In 2013, leaks from Edward Snowden revealed that the National Security Agency had wiretapped conversations of former President Dilma Rousseff, leading to several years of tense relations between the US and Brazil.
Bolsonaro, who has often expressed his admiration for the United States and Trump, said he was happy to visit Washington, particularly after decades of "anti-U.S." leaders in his country.
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.
In 2013, leaks from Edward Snowden revealed that the National Security Agency had wiretapped conversations of Rousseff, leading to several years of tense relations between the USA and Brazil.
"It seems to be, if it's conservatives, if Republicans, there is big discrimination", Trump said of social media platforms.
Before Tuesday's Oval Office meeting, Bolsonaro waived a visa requirement for USA visitors to Brazil and later in a Fox News interview on Monday night threw his weight behind Trump's immigration agenda, which includes a wall on the Mexican border.