The outgoing Ukip leader was speaking at a 15,000 supporter rally for Republican hopeful Mr Trump in Jackson, Mississippi.
Mr Trump, who is trailing his rival Hillary Clinton in the opinion polls, backed the UK’s exit from the EU.
In a tweet last week, Mr Trump said: “They will soon be calling me Mr Brexit.”
Mr Trump introduced Mr Farage as the man who “brilliantly” led the UK Independence Party’s campaign to secure a vote on the future of the UK’s 40-year membership of the European Union.
The majority of Mr Farage’s 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.
Mr Farage said: “Anything is possible if enough decent people are prepared to stand up against the establishment.”
He also condemned President Barack Obama’s decision to intervene in the EU referendum.
“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 in 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: “We did it – we made 23 June our independence day when we smashed the establishment. You can beat the pollsters, you can beat the commentators, you can beat Washington.”
Mr Farage, who attended the Republican convention in Cleveland last month, had previously said he would not “fall into the trap” of personally endorsing Mr Trump in his quest to reach the White House.
However, during his rally appearance he said that if he were an American, he would not vote for Mrs Clinton “even if you paid me”.
Trump called Farage’s appearance an honour and said: “The nation’s working people will take control again.”
Meanwhile a Ukip MEP bidding to succeed Nigel Farage has insisted she is putting forward no policies as part of her leadership campaign.
Diane James said she wants to “refresh and review” the party’s 2015 general election manifesto in her first 100 days should she become leader.
This would ensure Ukip is “fully prepared” if Prime Minister Theresa May calls an early general election, she added.
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