Viewed as a diplomatic coup in Westminster to be first through the door, the talks at the White House on Friday will be closely watched in Washington for clues about Trump's foreign policy.
May is keen to start talks on a US-UK free trade agreement for when Britain leaves the European Union, which is also likely to mean leaving Europe's single market and its 500 million consumers.
Trump has hailed the Brexit vote as "smart", believing it mirrors his own anti-establishment rise to the White House, but his calls for a protectionist trade regime could prove problematic for May.
The president's criticism of the EU and NATO have also caused alarm across the Atlantic -- as have his comments on torture, and plans to bar Muslims from entering the US.
May's first stop in the United States was Philadelphia where she was to address Republican Party lawmakers on a winter retreat, shortly after a speech by Trump.
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Both London and Washington have expressed their interest in a quick trade deal, although under EU rules Britain must wait until it has left the bloc before it signs deals with any other states.
May intends to start the two-year Brexit negotiations within weeks.
"There is much we can do in the interim, in terms of looking at how we can remove some of the barriers to trade in a number of areas," she told reporters on her plane.
The two leaders will also discuss counter-terrorism, the ongoing war in Syria, and the NATO military alliance which Trump deemed "obsolete" ahead of taking office last week.
Earlier this week, May spoke to NATO chief Jens Stoltenberg, expressing her support for the alliance and promising to take the message to Washington.
She will also emphasize the importance of enforcing the Iranian nuclear deal, which Britain helped negotiate and which Trump has denounced.
'Opposites attract'
Britain's second female prime minister, the reserved daughter of a vicar, has outwardly little in common with the outspoken US billionaire in the White House.
Asked about their contrasting personalities, May quipped that "sometimes opposites attract."
But Trump is highly controversial in Britain, not least for his comments on women, which May has described as "unacceptable."
She also had tough words on the president's position on torture, which he said Wednesday "absolutely" works.
"We condemn torture and my view on that won't change whether I'm talking to you or talking to the president," she told reporters.
Last January, parliament debated banning Trump from Britain after nearly 600,000 people signed a public petition, sparked by his promise to ban Muslims from the US if elected president.
"I will be representing the issues of everybody in the UK when I see Donald Trump," she added.
The premier said the importance of Friday's meeting is that "I will be able to talk direct to him and hear direct from him what his views are."
"We have a special relationship, it's a long-standing relationship, it's existed through many different prime ministers and presidents. I want to build on that relationship," she said.
May is taking a hamper of products from her official country residence, Chequers, for First Lady Melania Trump and a Scottish "Quaich" cup for the president, in honor of his Scottish roots.
