The Prime Minister is embarking on a two-day visit to the USA, which will see her become the first foreign leader to meet Mr Trump since his inauguration as president last week.
Addressing Republican congressmen in Philadelphia on Thursday, Mrs May will say changes in both the UK and US are renewing the long-time allies in ways which will allow them to “rediscover our confidence together” and “lead together again” in the world.
Friday’s meeting in the Oval Office will focus on priorities like a post-Brexit trade deal and co-operation on security issues like Syria, counter-terrorism and Russia.
Mrs May is expected to stress the value of international institutions like Nato, after Mr Trump declared the military alliance “obsolete” on the campaign trail.
Downing Street also hopes it will allow Mrs May to get to know Mr Trump and establish a “strong and productive working relationship” with the new president.
But Mrs May is coming under pressure to demonstrate Britain’s independence from the US over issues like gender equality, the environment and torture.
Mr Trump used his first TV interview since coming to office to assert his view that waterboarding of terror suspects - widely seen as a form of torture - “absolutely works”.
He is understood to be preparing to order a review of interrogation methods and the possible reopening of “black site” prisons outside the US.
Responding to concerns about Mr Trump’s plans on the eve of her departure, Mrs May assured MPs “we do not sanction torture, we do not get involved with that and that will continue to be our position”.
The PM’s official spokeswoman said Mrs May recognised there would be “issues where we differ in approach and view with President Trump” and believed a close relationship would allow her to “raise these frankly and directly with the president”.
But she declined to say whether the use of torture would be on the agenda on Friday.
Mrs May will tell congressmen on Thursday that withdrawal from the EU will give the UK “the opportunity to reassert our belief in a confident, sovereign and global Britain, ready to build relationships with old friends and new allies alike”.
Bracketing the Brexit vote with Mr Trump’s election, she will say: “As we rediscover our confidence together - as you renew your nation just as we renew ours - we have the opportunity, indeed the responsibility, to renew the special relationship for this new age.
“We have the opportunity to lead together again.”
She will tell them of her ambition to revive the shared leadership provided by the US and UK, which in the past had “made the modern world” and fulfilled “the promise of freedom, liberty and the rights of man”.
Mrs May is expected to hold private meetings with senior Republicans in Philadelphia before flying on to Washington DC for her face-to-face talks with Mr Trump.
Downing Street will be hoping the event will draw a line under the embarrassment of seeing Nigel Farage become the first UK politician to meet the then president-elect - who even proposed the former Ukip leader as an ambassador.
Before the meeting, Mrs May will lay a wreath at Arlington Cemetery, which is the resting place of a number of British troops who died fighting alongside US forces.
During Prime Minister’s Questions on the eve of her departure, former Labour leader Ed Miliband pressed Mrs May to tell Mr Trump to abide by the terms of the Paris Agreement on climate change, while the Scottish National Party’s Westminster leader Angus Robertson urged her not to make sacrifices on privatisation of healthcare or food safety to secure a trade deal with the US.
Senior Conservative Andrew Tyrie said she should make clear to the president that Britain will not facilitate torture.
Speaking ahead of the visit, former US assistant secretary of state James Rubin said America should not return to torture methods of interrogation.
He told the BBC: “The United States, at least until this president, prided itself on being a creator, and a supporter, of the rule of law in the world. We have operated successfully in the United States with multiple methods to succeed in preventing another 9/11 and I am confident that we can do that without the need to torture.”
JK Rowling sent a message warning the PM history will judge the stance she takes towards the new US president.
In a tweet sent as Mrs May left the UK, the Harry Potter author wrote: “History’s watching, Theresa.”
Rowling has been a vocal critic of Mr Trump, voicing concern in recent days over his order barring organisations receiving US aid cash from supporting abortion as a form of family planning.