The TV presenter and journalist warned critics not to “underestimate” the Mr Trump in the lead-up to his inauguration on Friday.
Morgan praised Mr Trump for his work so far and for assembling an “incredibly impressive” cabinet.
He told talkRADIO’s Julia Hartley-Brewer: “The guy's a businessman and he's filled the cabinet, not with career politicians or diplomats, but with some of the biggest dealmaking killers and military leaders imaginable.
Piers Morgan has called on Donald Trump's critics to stop "mocking" him
He can swing from the hip and say occasionally offensive things and he’s not Mr Perfect or an angel, nor from my experience of knowing him 10 years is he remotely a monster
“It's an incredibly impressive array of people. Do not underestimate Trump, he’s a brilliant delegator and a brilliant businessman.
“I think it’s time really to put aside all this kind of mockery, abuse, treating him like a joke. The guy is now – as from this afternoon – the most powerful man on earth.”
The TV personality urged the UK to get behind the billionaire tycoon in the wake of the Brexit vote.
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Nigel Farage and Donald Trump during the election campaign last year
“It’s in Britain’s interests now to forge as strong a relationship with him as we can, particularly I think since we’re now Brexiting and will need the Americans,” he said.
Speaking about Donald Trump’s past comments about women, Muslims and Mexicans, Morgan said he will judge the billionaire by his actions.
The President-elect had come under fire after a 2005 recording emerged during his election campaign of him making lewd remarks about women. He also vowed to build a wall at the US border with Mexico and ban Muslims from entering the United States.
He said: “I don't support things that I find personally offensive… [but] I take Trump on what he does.
“I happen to think it’s more prudent to give him an open mind now to see how actually performs as leader.
“Although he can swing from the hip and say occasionally offensive things and he’s not Mr Perfect or an angel, nor from my experience of knowing him 10 years is he remotely a monster and I happen to think he will surprise people.”