May, the reserved daughter of a vicar, has promised to be "frank" in her dealings with the unpredictable billionaire,
After igniting a row this week with Mexico over his plans to build a border wall, Trump will likely have an easier ride with May as she seeks to reaffirm Britain's "special relationship" with the United States with an eye on her country's future outside the European Union.
May arrived in the United States on Thursday and received a rapturous welcome from Republican lawmakers gathering in Philadelphia with a speech urging them to "beware" of Russia, and warning US allies to "step up" and play a greater role in global security.
She met with Republican House Speaker Paul Ryan and discussed issues that included early efforts to forge a trade deal for when Britain leaves the European Union.
May is hoping the prospect of a US deal -- while complicated -- will help dispel fears among a divided public that Britain may be economically worse off by leaving Europe's single market.
But her decision to meet Trump just one week after his inauguration has caused controversy at home, where he has been condemned by politicians of all guises for his comments about women, Muslims and the use of torture.
May, the reserved daughter of a vicar, has promised to be "frank" in her dealings with the unpredictable billionaire, and laughed off questions about their personal compatability.
"Haven't you ever noticed that sometimes opposites attract?" she told reporters on her plane.
The pair will meet at the White House and hold a joint press conference before taking part in a working lunch.
It will be the first such event for the president since taking office.
May will begin her day Friday with a visit to Arlington National Cemetery, the final resting place of a number of British soldiers who died fighting alongside US forces in various wars.
The prime minister's speech to Republican lawmakers on Thursday hailed strong security ties between the two countries, and said their relationship had "defined the modern world."
May said NATO member states should contribute their fair share -- a complaint made by the former and current US administrations -- but defended the alliance from Trump's claims it was "obsolete."
May also defended the Iranian nuclear deal against the president's criticism, saying it was "vitally important" for regional security -- but must now be properly enforced.
The prime minister had tough words on Trump's assertion that torture "absolutely" works, telling reporters that she condemned the use of illegal interrogation.
However, she won loud applause from Republicans when she praised Trump's victory, which he has compared to the anti-establishment feeling that drove the Brexit vote last June.