Trump hailed the monarch as a "great man" and said the royal couple's trip would be "a positive" in an interview with the BBC.
He also warned he does not think UK Prime Minister Keir Starmer has a chance of repairing the relationship unless he changes direction.
As well as policy differences, the two leaders have been at loggerheads over the Middle East conflict, with the president deriding the prime minister as weak and indecisive.
Charles, accompanied by his wife Queen Camilla, will kick off the four-day trip on Monday with a private tea with Trump before addressing Congress, a state dinner and visits to New York and Virginia.
Buckingham Palace has said he will not be meeting any survivors of Jeffrey Epstein.
Charles' brother, Andrew Mountbatten-Windsor, was arrested in February on suspicion of leaking government documents to the late US sex offender.
The former prince Andrew has denied any wrongdoing.
Asked by the BBC whether the King's trip will help repair strained transatlantic relations, Trump said: "Absolutely. He's fantastic. He's a fantastic man. Absolutely the answer is yes.
"I know him well, I've known him for years.
"He's a brave man, and he's a great man. They would absolutely be a positive."
Trump also earlier this week waded into the row over Peter Mandelson and his appointment as US ambassador, branding it "a really bad pick" but added that Starmer had "plenty of time to recover".
The royal state visit marks the 250th anniversary of the US declaration of independence from British rule, when the then 13 American colonies decided to split from King George III, Charles's five-times-great-grandfather.
For Charles, it will be a moment to reflect on how the UK and the US have come together since then to forge some of the world's closest security, military and economic ties while for Trump it will be another chance to indulge his love of the royals.
Nigel Sheinwald - UK ambassador to the US from 2007 to 2012 - said the visit could not, and was not designed to heal any current acrimony between governments but it would demonstrate ties that went far deeper than any individuals.
"Pretty much more than any other visit, this is about the long term. This is about the fundamentals of the relationship between our peoples, our countries," Sheinwald told Reuters.
"It's not about what's going on today."
Royal aides privately say Trump behaved impeccably during his unprecedented two state visits to the UK in 2019 and last year.
"He is a huge royalist," royal biographer Robert Hardman told Reuters.
"He has ... one mindset when it comes to the British government but British monarchy is a completely separate element, and he's a huge fan of it. And he adored the late queen, a big fan of the King. For him, this is a big moment."
with PA
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