Trump and US First Lady Melania Trump touched down in their Air Force One at Stansted Airport in the east of England from the North Atlantic Treaty Organisation summit in Brussels.
"Brexit is Brexit, the people voted to break it up so I would imagine that is what they'll do, but they might take a different route, I'm not sure that's what people voted for", Trump said, adding: "They're great people - I just want them to be happy".
"Our trade and investment relationship is unrivalled - we are the largest investors in each other's economies and every day a million British people go to work for U.S. companies in the United Kingdom and a million Americans go to work for United Kingdom companies in the U.S.", May said. "We have come to an agreement which absolutely delivers what people voted for", she said in a statement.
Trump has always been a supporter of Brexit and has expressed enthusiasm for a wide-ranging trade deal with Britain after it leaves the European Union, something heralded by Brexit supporters as being one of the great benefits of exiting the bloc.
Allies are concerned Trump won't be tough with Russia's president or even raise the issue of election meddling.
He has also said he might speak to Boris Johnson, who quit as foreign secretary over May's plans.
Some Brexit supporters have cast May's Brexit plan as a betrayal, including MPs in her own deeply-divided party who have warned of a leadership challenge.
May hopes Trump, who arrived at Stansted airport from Brussels, will help accelerate a future free trade deal, though his public comments on Brexit have cast a shadow over the visit.
Queen Elizabeth II has outlasted 13 United States presidents during her reign.
Many Britons are opposed to Trump's trip which is not the full state visit he was originally promised with the pomp and ceremony that entails.
"When we leave the European Union we will begin to chart a new course for Britain in the world and our global alliances will be stronger than ever", May said ahead of Trump's visit.
Shrugging off the plans for mass protests, which on Friday will include a giant baby-shaped blimp bearing Trump's features, he said in Brussels: "They like me a lot in the UK".
"The United States commitment to North Atlantic Treaty Organisation is very strong", he said.
This is when huge protests will be held across the city, with 50,000 people expected to turn up on Friday afternoon - parading to Trafalgar Square through central London.
Khan gave protesters permission to fly the 20-foot-tall balloon depicting Trump as an angry baby in a diaper.
A campaign is also underway to get "American Idiot", a 2004 song by the US punk rock band Green Day, to the top of the UK Singles Chart.
Before the Sun interview was published, May invoked Winston Churchill as she addressed Trump and business leaders at a black-tie dinner at Blenheim Palace, the grand 18th-century country house which was the British World War Two leader's birthplace.
On Friday, Trump will meet up again with May for a visit to an undisclosed military site before traveling to Chequers, her country estate, for talks on a range of issues.
Over a lunch of Dover sole, lamb and lemon meringue pie, the leaders will discuss Russian Federation, trade, Brexit and the Middle East.