The US president-elect hosted the euro-sceptic leader at his New York residence Trump Tower where they spent over an hour discussing the Republican's "victory, global politics, and the status of Brexit", according to a UKIP statement.
The meeting will be seen by some as an embarrassment for British Prime Minister Theresa May who spoke with Trump by telephone this week, but has yet to meet him in person.
Downing Street has denied reports that Farage will act as a "go-between" in British relations with the new US administration.
Farage stressed the importance of the Anglo-American relationship and asked Trump to return the bust of former British prime minister Winston Churchill to the Oval Office, the statement said.
The interim-UKIP leader said it was "a great honour" to spend time with Trump, describing him as "relaxed, and full of good ideas".
"I'm confident he will be a good president," Farage added.
"His support for the US-UK relationship is very strong. This is a man with whom we can do business".
Farage threw his support behind the billionaire businessman during the US election campaign, attending a rally in Jackson, Mississippi in August and likening it to his own campaign to leave the European Union.
The shock outcome of the US election prompted many commentators to draw parallels with Britain's June 23 referendum after Trump said the vote would be "Brexit plus plus plus".
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