Trump and May will start the day by co-hosting a breakfast meeting of British and American business leaders at St James's Palace in a bid to boost trade links, the BBC reported.
The Duke of York, Chancellor Phillip Hammond, US Secretary of State Mike Pompeo and the President's daughter Ivanka Trump are also expected to attend.
May, who will stand down as Conservativeleader on Friday, will then hold talks with the US President in Downing Street, when they are expected to discuss a range of issues including climate change and the Chinese tech giant Huawei, which the US has blacklisted for security reasons.
Also on Tuesday, thousands of people are expected to join protests against Trump's visit.
A "national demonstration" in London's Trafalgar Square will start at 11 a.m., while protests are also planned in Birmingham, Stoke, Sheffield, Glasgow, Edinburgh, Chester, Leicester, Oxford and Exeter.
Organisers have called for a carnival atmosphere, but a huge police operation is taking place in central London to prevent any disruption to the trip.
Opposition Labour Party leader Jeremy Corbyn is due to address the London rally, where he will be joined by members of other political leaders.
The President and First Lady Melania Trump arrived in London on Monday. He later praised the "eternal friendship" between the UK and US during a state banquet at Buckingham Palace hosted by Queen Elizabeth II.
But before touching down, the President reignited his political feud with the Mayor of London, calling Sadiq Khan a "stone cold loser".
( With inputs from IANS )