It was the first-ever visit to Brazil by an Israeli prime minister.
Netanyahu is also expected to hold talks with top officials from Brazil and other countries during his trip.
Netanyahu left for Brazil earlier on Thursday, where he will attend Bolsonaro's inauguration, and will also meet with him and with the country's defense and foreign ministers.
The Trump administration sees a strong ally in Bolsonaro, who is following the lead of the United States in moving Brazil's embassy in Israel to Jerusalem and has been critical of worldwide efforts to fight climate change.
Rio de Janeiro: Brazilian President-elect Jair Bolsonaro and Israeli Prime Minister Benjamin Netanyahu here on Friday agreed to establish a strategic partnership between the two countries.
But there was no mention of Bolsonaro's post-election declaration of the embassy move during Friday's press conference.
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Both the Workers' Party and the Socialism and Liberty Party said the decision was also an act of resistance to Bolsonaro, who has angered many with comments seen as homophobic, racist or offensive to women, as well as expressing nostalgia for Brazil's 1964-1985 military dictatorship.
"It's hard to believe that we had no such contacts before", he said. Trump's National Security Advisor John Bolton said the U.S. president and Bolsonaro were "like-minded" individuals.
Netanyahu said that his visit to Brazil "heralds a historic moment". "Our cooperation will help the citizens of both countries in economy, technology and military areas and will help strengthen the worldwide status of Israel", Netanyahu said after the meeting with Bolsonaro, as quoted by his office in the statement.
The Palestinians view East Jerusalem as the capital of their future state, and most countries in the world back a longstanding consensus that Jerusalem's status can only be resolved through negotiations and as part of an Israeli-Palestinian peace process. For example, trade volume in 2017 between the two countries reached more than $1.1 billion.
United States allies including Israel were caught by surprise by Trump's abrupt announcement last week that he was pulling USA troops out of Syria, where Israel's arch-foe Iran has built up a significant military and political presence.
In preparation for his tenure as president, Bolsonaro has sent aides to Israel to study desalination technology and to investigate the potential purchase of drones for use by Brazilian security forces.
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The family had moved to Cairo, Egypt, in order to escape civil war in Yemen when Abdullah was eight months old. Abdullah had been on life support, but his condition was fatal and doctors had given him only days to live.