Mrs May will be the first foreign leader to meet the new president after his inauguration.
A post-Brexit free trade deal is thought likely to be high on her agenda as she travels to the US for talks.
Confirmation of the meeting came as hundreds of thousands of people around the world joined women's marches to protest Mr Trump's presidency.
Mr Trump's press secretary Sean Spicer gave details of Mrs May's visit in his first briefing to journalists at the White House on Saturday.
Earlier, while visiting the CIA's headquarters, President Trump said the PM "is coming over to our country very shortly".
Nato, the European Union, defence and Russia are all likely to be discussed in the meeting.
The BBC's political correspondent Iain Watson said the "symbolism will be very important" and with Brexit negotiations about to get under way, the fact Mrs May will be meeting the new president so soon will be "politically significant".
Our correspondent said there had been a lot of effort to make sure Mrs May was one of the first leaders President Trump would meet.
In December the PM's joint chiefs of staff, Nick Timothy and Fiona Hill, travelled to the US to build links with the incoming president's team ahead of his inauguration on 20 January.
Theresa May congratulates Trump on taking office
In a statement issued after the inauguration, Mrs May said: "From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic.
"I look forward to discussing these issues and more when we meet in Washington."
Mrs May has promised to hold "very frank" discussions with Mr Trump.
She told the Financial Times she believed the new president recognised the importance and significance of Nato and the "importance of the co-operation we have in Europe to ensure our collective defence and collective security".
On the day after his inauguration, at least 500,000 people gathered for a rally outside the US Capitol building in Washington while organisers said an estimated 100,000 descended on central London on Saturday as similar events were staged in major cities across the US and around the world.

In 2013 a working group, set up by the Scottish government, recommended eligible couples should be offered up to three treatments.
But that would only be after health boards had reduced IVF waiting times.
Infertility Network UK said it was a "no-brainer" there should now be three cycles as waiting times have fallen.
New IVF criteria was introduced in July 2013, following recommendations by the National Infertility Working Group.
The changes were designed to standardise fertility treatment across Scotland to prevent a "postcode lottery".
Giving evidence to Holyrood's health committee, the charity's chief executive Susan Seenan said: "The group recommended three cycles and said that once the waiting times were down to below 12 months, at the latest early 2015, they would consider moving to three cycles.
"It just doesn't seem to be happening as fast as we would like it to.
"We just think now that the waiting times are down, that it is a no-brainer - we should move to offering everybody who is eligible three cycles."
Susan Seenan added: "Everybody in the group was agreed that...three cycles was the best possible way to move forward for patients.
"Why anybody would not want to move forward with that, I have no idea, unless it is finance related."
A spokeswoman for the Scottish government said Scotland was "leading the way" in the provision of NHS IVF treatment, with Â£12m of investment over the last three years.
She said the number of IVF cycles that couples were entitled to was under review.
The spokeswoman added: "The reconvened expert group has met twice and its review will consider a range of issues, including the number of IVF cycles, to ensure access to IVF treatments remains fair, reliable and timely.
"The views of patients and our stakeholders, including Infertility Network Scotland who are part of the Infertility Group, will be instrumental to this process, along with data collection and modelling."
Fertility treatment is currently available to those under 40, and is not offered to women who are obese.
In addition, couples need to have been in a stable relationship for two years and neither partner can smoke for three months before treatment begins.
Both partners also need to be methadone-free for a year before IVF starts.
Women aged between 40 and 42 are eligible for one cycle of fertility treatment if they have never previously undergone the procedure.
Prime Minister Theresa May will meet US President Donald Trump in Washington DC on Friday, the White House has said.
[NEXT_CONCEPT]
A charity is calling for couples in Scotland who need help conceiving to have access to three cycles of IVF instead of two.