The private audience with the pontiff was preceded by a cordial handshake for the cameras and was expected to last around 20 minutes.
It came on the third leg of Trump's first overseas trip as president, which has already taken him to Saudi Arabia and to Israel and the Palestinian territories.
The two men had never met before Wednesday morning but they have significant history having clashed publicly over subjects ranging from migration to unbridled capitalism and climate change.
Trump was accompanied for the audience by his wife Melania and daughter Ivanka, both dressed all in black, in keeping with traditional protocol that is no longer always observed by all female dignitaries visiting the Vatican.
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The audience took place in the private library of the Apostolic Palace, the official papal residence that Francis does not use, having opted instead for modest lodgings in a Vatican guesthouse.
Immediately after the meeting, the 80-year-old pope was due to give his usual midweek address to the faithful on St Peter's square while the Trump couple are given a private tour of the Sistine Chapel and St Peter's Basilica.
The Trump team is due to fly to Brussels on Wednesday afternoon for meetings with EU and NATO officials before returning to Italy late Thursday for the G7 summit in Sicily on Friday and Saturday.