Trump's morning audience with Francis will come just days before he is scheduled to attend a G7 summit meeting in Sicily.
It will be followed by meetings with his Secretary of State Pietro Parolin and Archbishop Paul Gallagher, Secretary for Relations with States.
The two leaders have previously staked out opposing policy positions, most notably in a heated exchange through the media while Trump was campaigning in February 2016 to become the Republican Party's nominee for the White House.
"Anyone, whoever he is, who only wants to build walls and not bridges is not a Christian," Francis told journalists, responding to a question about the real estate mogul's anti-immigrant stance.
Trump retorted: "For a religious leader to question a person's faith is disgraceful."
He also commented: "If and when the Vatican is attacked by Isis, which as everyone knows is Isis's ultimate trophy, I can promise you that the Pope would have only wished and prayed that Donald Trump would have been President. [sic]"
Trump later softened his tone, saying the pope was misinformed, unaware of the impact of the drugs coming into the United States and a range of security issues that made it necessary to build a wall along the southern US border.
On a visit to Mexico in February 2016 Francis held an open-air mass on the US-Mexico border, where he described forced migration as "a human tragedy."
More recently, in an interview with Spanish daily El Pais conducted as Trump was being sworn in as president on January 20th, Francis warned against populism, saying it could lead to the election of "saviours" like Hitler.
He also condemned the idea of using walls and barbed wire to keep out foreigners.
Just days after his inauguration, however, Trump took a first step toward fulfilling his pledge to build a 2,000-mile (3,200 kilometres) wall along on the Mexican border, signing two immigration-related decrees.
His administration has also tried to impose travel bans for people from seven mostly-Muslim countries as well as all refugees, a move directly at odds with Francis's calls for welcoming and integrating people forced from their homes. The pontiff has personally housed refugees in the Vatican, as well as encouraging priests to welcome migrants in their parishes.
The pope has also been an ardent supporter of efforts to combat climate change and its consequences to the world's most vulnerable populations, in terms of pollution, disease, wars and migration.
In November he criticized politicians who have yet to show "concrete will" in implementing global climate agreements.
The comments were seen by many as a swipe at Trump's pledge to pull the United States out of the COP21 Paris Agreement which binds countries to national pledges to reduce greenhouse gas emissions.Trump has said he will make his decision on sticking to the agreement before the G7 meeting in Taormina, Sicily.
But there could be areas for the two leaders to find common ground, in particular over Trump's efforts to curb abortions. He has signed legislation that removes Obama-era rules protecting tax-funded financing of family planning clinics that offer abortions.
Last month, Trump said he was looking "very much forward" to meeting with Francis, and it appears that both sides made an effort to make the meeting happen.
Leaders normally give the Holy See several months' notice when requesting a papal audience, but both Vatican and White House officials said they were trying to arrange a meeting.
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Photo: Jim Watson/AFP