In his first British interview with 'The Times' newspaper, the billionaire-businessman-turned-politician also promised that a trade deal between the US and UK will be signed "very quickly" under his presidency.
"I think Brexit is going to end up being a great thing," Trump said yesterday on Britain's referendum vote in June last year to leave the 28-member bloc.
Trump was interviewed for The Times by former UK justice secretary Michael Gove, a writer and MP from Britain's ruling Conservative Party who was a leading figure in the anti-EU campaign.
Asked specifically about a potential US-UK trade deal, he said: "Absolutely, very quickly. I am a big fan of the UK, we are gonna work very hard to get it done quickly and done properly. Good for both sides.
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Outgoing US President Barack Obama had said in April last year that the UK would be "at the back of the queue" if it quit the EU.
Trump dismissed that statement, saying: "Obama said, 'They'll go to the back of the line,' and then he had to retract his statement."
Gove, a prominent Leave campaigner during last year's referendum on Britain's membership of the EU, is also a columnist for the 'Times'.
Trump blamed the decision of German Chancellor Angela Merkel to welcome refugees fleeing war in the Middle East, for jeopardising the stability of Europe.
"I think she made one very catastrophic mistake and that was taking all of these illegals, you know taking all of the people from wherever they come from. And nobody even knows where they come from," he said.
In the simultaneous interview with German newspaper 'Bild', Trump said he might contemplate tightening restrictions on Europeans wanting to travel to the US.
provocative comments about foreign policy, reiterating that he could do a deal with Russia that would result in sanctions being lifted and described the NATO military alliance as "obsolete".
"I said a long time ago that NATO had problems. Number one it was obsolete, because it was designed many, many years ago. Number two the countries aren't paying what they're supposed to pay. I took such heat, when I said NATO was obsolete.
It's obsolete because it wasn't taking care of terror," he said.
Trump also made a reference to his Scottish-born mother's admiration for the UK and its monarch as a sign of the kind of relationship he wants with Britain under his presidency.
He also revealed that May had written to him just after Christmas with a gift of a copy of Winston Churchill's address to the American people shortly after the Japanese attack on Pearl Harbour which marked America's entry into World War II.
In the letter, the British Prime Minister told Trump that she hoped the sentiment of "unity and fraternal association" between the two countries was "just as true today as it has ever been".