Bolsonaro's arrival in Florida ended days of confusion over his whereabouts, after he was reported to have travelled to Argentina, and then prematurely reported to have already entered the US on Tuesday.
In a statement, Bolsonaro thanked both the presidents of Argentina and the US, and the American public "who share the same values as the good people of my own country".
"It was never my intention to leave my homeland, but I know exactly where this is heading," he said. "I departed from a regime of exception so that I could become the leader my people deserve."
He called himself a victim of a coup d'état and political persecution, and said his travel to the US was to protect his family.
In the lengthy letter, he also repeated unsubstantiated allegations of "electoral fraud" which he said allowed a "mathematical impossibility" to occur in the election.
On Wednesday, Trump declined to discuss the allegations made in Bolsonaro's letter.
"I won't get involved.…