The US said it would work to provide support for a fund to protect the Amazon rainforest and Biden agreed to travel to Brazil, according to a joint statement released by Brazil following Lula's first visit to Washington since his election win.
The two leaders also spoke of shared values in fighting climate change and protecting democracy against a rise in authoritarianism.
"We have to continue to stand up for democracy and our democratic values that form the core of our strength," Biden told Lula before a private Oval Office session between the leaders, adding that the two were on the "same page" about the "climate crisis".
Bolsonaro enjoyed vocal support from former US president Trump, a Republican, but Brazil's diplomatic relations cooled with other traditional allies during the far-right leader's presidency.
Bolsonaro flew to Florida two days before his term ended on January 1, having challenged the results of the October 30 runoff election he narrowly lost to Lula.
Days later, a violent movement of election-denying Bolsonaro supporters stormed Brazil's presidential palace, Congress and Supreme Court.
Brazil "self-marginalised itself for four years" under the former president, Lula said at the White House, without mentioning Bolsonaro by name.
His world, Lula said, had "started and ended with fake news in the morning, afternoon, at night", prompting Biden to laugh and interject "sounds familiar".
Lula said Brazil was trying to reposition itself in the world and both countries should never again allow the kind of attacks like the one by Bolsonaro supporters last month or the one it echoed at the US Capitol on January 6, 2021.
Lula said the two leaders could also work together to combat inequality and climate change.
For all the bonhomie, the leaders were not expected to agree on the war in Ukraine, given Brazil's neutrality.
Lula wants to see a negotiated discussion of peace with the involvement of more neutral global players, a position he said he discussed with Biden, adding that he sensed from Biden the same interest in ending the war.
The Brazilian leader also defended his decision not to provide German-made artillery ammunition sought for the West's support of Ukrainian defence.
"If I sent the ammunition, I would be joining the war. I don't want to join the war. I want peace," he said earlier on CNN.
Biden and Lula agreed to work together on reforming the United Nations Security Council to include "permanent seats for countries in Africa and in Latin America and the Caribbean", according to the joint statement.
During the trip, Washington agreed to work with Congress to provide "initial support" for the Amazon Fund started by Germany and Norway to back the protection of the rainforest and sustainable development projects, according to a joint statement.
The US plans an initial donation of $US50 million ($A72 million), according to a Brazilian source, underlining the resetting of ties between the two countries after the recent period of frosty relations.
Brazil has been eager for more countries to contribute.
The new Lula administration signaled its commitment to protecting the Amazon rainforest this week by launching an enforcement operation against illegal gold miners that have devastated the Yanomami indigenous reservation in northern Brazil.
