The outgoing Ukip leader was speaking at a rally for Republican White House hopeful Mr Trump in Jackson, Mississippi.
The majority of his speech focused on the success of the campaign for Britain to leave the EU.
He framed it as a victory for the anti-establishment movement – a theme that is also popular in Mr Trump’s campaign. Populist movements across the world have made major campaigns within their countries, and advancements such as UKIP and presidential nominee Donald Trump have also motivate some in parts of Europe.
He said: “Anything is possible if enough decent people are prepared to stand up against the establishment.”
Mr Farage condemned President Barack Obama’s decision to intervene in the EU referendum and urge Britons to vote Remain.
“I could not possibly tell you how to vote in this election,” he said. “But I will say this, if I was an American citizen I wouldn’t vote for Hillary Clinton if you paid me.”
Earlier, on a visit to Florida, Mr Trump said polls showed him trailing the state.
Mr Farage told the audience at the Mississippi Coliseum that they could challenge the expectations of pollsters as Brexit campaigners had.
He said that he came to the UK with a message of hope that “the little people” could “overcome” big banks and multinationals.
He said: “We did it – we made June 23 our independence day when we smashed the establishment.”