The defeated right-wing candidate has flown to the US - thanking Donald Trump and "the wonderful American people for welcoming me".
The 45-year-old senator said his victory was denied because of an electoral coup d'etat by his left-wing rival President Luiz Inacio Lula da Silva, who unexpectedly surged ahead.
Mr Bolsonaro claimed there has been a "politically motivated witch-hunt, intended to hold me hostage".
He did not give any evidence for the alleged electoral fraud.
Lula's victory has been recognised by global leaders, international observers and Mr Bolsonaro's own party - with Brazil's electoral authority saying the vote took place in full compliance with legal and constitutional requirements.
The defeated candidate landed in Miami on Wednesday morning after travelling from South America on a private jet.
"Faced with the politicisation of the justice system in Brazil, I brought my family to the United States, where we are safe," Mr Bolsonaro said.
He insisted he did not flee his country and left "so I could be the leader my people deserve" - adding he would "lead the opposition from here".
Mr Bolsonaro made his comments in an open letter shared with journalists by his allies, Reuters reported.
He later deleted the letter, in which he called himself "president-elect of Brazil", from social media and quickly published a new document calling himself the "leader of Brazil".
Mr Bolsonaro said in the updated version: "I want to say, not only to my 60 million voters but to the Brazilian people, that I am the leader and that the criminals who stole Brazil's election are part of a criminal organisation that has established a tyranny."
Lula won a historic fourth term in a surprise result that defied polls and the left-wing candidate described reports his opponent had left the country as "shameful".
Mr Bolsonaro has refused to concede following defeat in the run-off vote and threatened to attempt to annul the election result.
He was ordered by Brazil's Supreme Court to surrender his passports to federal police as part of a probe into alleged money laundering, which he denies.
But he instead followed his father, jailed former president Jair Bolsonaro, who also fled to Florida after losing the 2022 presidential election to Lula.
Flavio Bolsonaro and his family crossed into Argentina via the Tancredo Neves International Bridge border crossing, before boarding a private flight bound for Ecuador, according to Argentina's migration department.
The senator appeared to be "distraught and fearful" of being arrested after his shock defeat became clear, news outlet O Globo said.
Voting was neck and neck throughout Sunday evening's count before Lula, 81, pulled away to secure an unprecedented fourth term in office.
With almost 100% of the votes counted, Brazil's electoral court said Lula had secured 51.79% of the ballots cast, to Mr Bolsonaro's 48.21%.
But Mr Bolsonaro refused to accept defeat and asked for the election results to be annulled after voting time had been extended by two hours by a Supreme Court judge. He said the extension was "unacceptable".
President Lula won by about 4.5 million votes and it is believed fewer than 35,000 ballots - 0.03% of the total - were cast during the additional two hours of voting.
Mr Trump did not endorse Mr Bolsonaro ahead of the vote, but said on Monday the results "looked like another rigged election" without providing evidence.
Lula's victory was all the more remarkable given that Mr Bolsonaro beat him by 2.2 million votes in the first round of the election earlier this month.
The US central bank confirmed rates will remain at about 3.9% following a two-day policy meeting - with the announcement coming just days before the midterm elections taking place next week.
Fed chair Kevin Warsh did not confirm if rates would increase later this year - a move many economists are predicting - but insisted that holding rates now would allow for "the accumulation of more information" for future decisions.
Last month, the Fed hiked interest rates for the first time in three years, prompting an angry response from Mr Trump, who said the benchmark rate should be lowered to "1% or less".
The US president told reporters that rates were "too high" and "not appropriate" - adding that "we should be paying the lowest interest rates, because we have the strongest credit".
Despite tensions with the White House, Mr Warsh - speaking at a news conference on Wednesday - insisted "politics played no role" in the decision to keep interest rates unchanged.
US inflation, which rose to 3.7% in September, has accelerated in recent months as the Iran war has caused spikes in oil and gas prices.
It has led to concerns around the high cost of living - including groceries, petrol and housing - becoming a key focus of the upcoming midterm elections.
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Mr Warsh underscored the Fed's aim to bring inflation down to its 2% target, saying: "Energy and related prices have moved higher again in recent weeks.
"Our job is to ensure that relative price changes in some sectors do not broaden out across the economy."
It remains to be seen what impact the Fed's decision to leave interest rates on hold will have on the Bank of England, which meets next month.
In September, the Bank voted to keep rates at 3.75% - but economists are expecting a hike in borrowing costs before the end of the year in an attempt to tackle rising prices.
UK Prime Minister Andy Burnham has previously said that addressing the cost of living crisis is one of his key priorities.
Mr Trump is seeking damages over the editing of a Panorama documentary concerning the US Capitol riots, which aired in 2024.
However, a court in Miami has this week ordered the US president to produce the relevant documents by 23 November or risk the case being thrown out.
US Magistrate Judge Enjolique Lett said that "failure to comply with this order could result in sanctions, including but not limited to, dismissal of this action for failure to prosecute this case".
Judge Lett also said that, in the absence of a register identifying any documents which had been withheld due to claims of privilege, Mr Trump must compile a list by 5 November.
In her ruling, the judge voiced concerns over whether "an adequate search for all responsive documentation" by Mr Trump's legal team took place.
The BBC has accused Mr Trump of flouting the rules by failing to disclose documents as part of the case.
Lawyers for the corporation asked the court to intervene, arguing it would "experience extreme prejudice" if the president "continues to disregard his discovery obligations".
They said the ongoing delay related to documents "that are not in dispute" and which Mr Trump had previously agreed to disclose.
Mr Trump has previously tried to block the release of his financial records as he sought to change his complaint and limit disclosure. However, this appeared to be a separate matter as the production of these papers was contested.
Last week, Judge Lett ordered the president to sit for deposition by 11 December after he cancelled an agreed date of 16 October, citing "matters of national importance".
The BBC has argued Mr Trump is attempting to delay his appearance until January next year.
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'Error of judgement'
Trump: A Second Chance? was broadcast by the BBC days before the 2024 US presidential election.
The programme spliced together two sections of the president's speech into what appeared to be one quote.
Mr Trump's lawyers say the programme falsely portrayed the president as a "violent insurrectionist", caused "massive economic damage to his brand value" and was a "brazen attempt" to interfere in the US election.
The allegations led to the then-BBC director-general Tim Davie announcing his resignation.
Samir Shah, the BBC chairman, apologised on behalf of the broadcaster over what he called an "error of judgment" and accepted the editing of the programme gave "the impression of a direct call for violent action".
However, the BBC is seeking to have the case dismissed, warning of the "chilling effect" it would have on "robust reporting on public figures and events".
The corporation has also challenged the jurisdiction of a Florida court to hear the case given the programme was never aired in the US.
Police said the girl had been inside an enclosure with a staff member and two other children when the attack happened at the Johannismühle wildlife park in Brandenburg, near Berlin, on Wednesday.
She was taken to hospital by helicopter after being attacked by at least one animal and suffering head injuries, according to German newspaper Bild.
No one else was hurt in the attack.
In a statement, police said that the "exact circumstances of the incident are under police investigation, which is ongoing".
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German media reported that the incident happened before the park opened, and that the girl may have been taking part in a special visit.
The park, located in the town of Baruth/Mark, has been temporarily closed and is set to reopen on 2 November, according to its website.
Johannismühle offers small group tours and "exclusive" visits, with the opportunity to "feed wolves" mentioned on its site.
The park keeps grey and arctic wolves, along with other animals including the brown bear and lynx.
The incident comes after a number of other animal attacks at zoos and wildlife parks across Europe in recent weeks.
On Tuesday, a zookeeper died after being attack by a leopard on Saturday at the Beekse Bergen safari park in the Netherlands.
Earlier this month, a 24-year-old man died after entering a tiger enclosure at Yorkshire Wildlife Park in the UK.
The actress died in August after being found unresponsive in an apartment in the South Carolina city of Greenville.
Panettiere's on-and-off boyfriend Brian Hickerson and his brother Zach were in the property at the time.
Paramedics performed CPR and other resuscitation efforts for 40 minutes before declaring her dead.
Officers initially said there did not appear to be any signs of foul play - an assessment backed up by last month's post-mortem.
The coroner ruled Panettiere died from the toxic effects of an accidental overdose of several drugs, including the synthetic opioid fentanyl.
They found no signs of any physical trauma that would have contributed to her death.
The other drugs found in her system were 4-ANPP (fentanyl's chemical by-product), anti-anxiety medicine Alprazolam, muscle relaxer Methocarbamol, and Quetiapine - which can be used to treat severe depression.
Panettiere had been in rehab a few weeks before death, according to the coroner's report.
The 36-year-old found fame in the series Heroes, which ran from 2006 to 2010, and followed that with a role in Nashville, another hit TV programme.
She was involved in the entertainment world from a young age, appearing in adverts at just 11 months old and becoming a child actor.
Panettiere opened up about her struggles with postpartum depression and addiction in her memoir This Is Me: A Reckoning, which came out earlier this year.
She said it had led to her decision - in 2018 - to give custody of her daughter to her former partner, Ukrainian boxer Wladimir Klitschko, so she could get help.
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In an interview with podcaster Jay Shetty after the book's release, Panettiere said: "I think there's been this very common misconception that I just gave up my child. That could not be farther from the truth."
She described herself as being in a "horrible cycle for years of battling depression and anxiety and alcoholism and substance abuse" while "just trying to find my way back".
She also wrote about the pain of losing her brother Jansen, who died in 2023 from an undiagnosed heart condition.
Anyone feeling emotionally distressed or suicidal can call Samaritans for free on 116 123 or visit samaritans.org in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.