Mr Trump will also meet Italy's president and prime minister, before flying to Brussels for a Nato summit.
He earlier vowed to help Israelis and Palestinians achieve peace, as he ended the Middle East leg of his tour.
The US leader began his foreign trip with a two-day stop in Saudi Arabia over the weekend, urging Muslim countries to take the lead in combating radicalisation.
Mr Trump arrived at the Vatican just before 06:30 GMT for his meeting with Pope Francis. Afterwards, he will hold talks with Italian President Sergio Mattarella and Prime Minister Paolo Gentiloni.
It is hard to think of two more contrasting characters than Pope Francis and President Trump.
On one hand, the Jesuit who has made his mission the championing of the poor and dispossessed; on the other the property developer who has championed getting rich, and surrounded himself with billionaires in his cabinet.
And though this will be their first meeting they've already sparred. During the election the Pope on a visit to the Mexico-US border said that people who only think of building walls instead of bridges were not Christian.
Donald Trump described those comments as disgraceful, and accused the pontiff of being a pawn of the Mexican government.
But on Wednesday both men will be seeking to find common ground.
After his visit to Saudi Arabia, home to Islam's holiest sites, and to Israel, this is the final leg of the tour of the world's three great religions.
President Trump's commitment to fighting extremism and intolerance will win approval from the Pope, as will his determination to bring peace to the Middle East.
And the president thinks there's another reason why they will get on. Back in 2013 he tweeted: "The new Pope is a humble man, very much like me."
More about: #Trump-Pope
